Circuits

(E) The equivalent resistance through path ACD is equal to the equivalent resistance through path ABD, making the current through the two branches equal

A 9-volt battery is connected to four resistors to form a simple circuit as shown above. How would the current through the 2 ohm resistor compare to the current through the 4 ohm resistor? (A) one-forth as large (B) one-half as large (C) four times as large (D) twice as large (E) equally as large

(D) The resistance in each of the two paths is 9 Ω, making the current in each branch 1 A. From point A, the potential drop across the 7 Ω resistor is then 7 V and across the 4 Ω resistor is 4 V, making point B 3 V lower than point C

A 9-volt battery is connected to four resistors to form a simple circuit as shown above. What would be the potential at point B with respect to point C in the above circuit? (A) +7 V (B) +3 V (C) 0 V (D) -3 V (E) -7 V

(C) P = V²/R

A hair dryer is rated as 1200 W, 120 V. Its effective internal resistance is (A) 0.1 Ω (B) 10 Ω (C) 12 Ω (D) 120 Ω (E) 1440 Ω

(A) P = IV

A heating coil is rated 1200 watts and 120 volts. What is the maximum value of the current under these conditions? (A) 10.0 A (B) 12.0 A (C) 14.1 A (D) 0.100 A (E) 0.141 A

(D) P = IV

A household iron used to press clothes is marked "120 volt, 600 watt." In normal use, the current in it is (A) 0.2 A (B) 2 A (C) 4 A (D) 5 A (E) 7.2 A

(B) For more light at a given voltage, more current is required, which requires less resistance. R =ρL/A

A junior Thomas Edison wants to make a brighter light bulb. He decides to modify the filament. How should the filament of a light bulb be modified in order to make the light bulb produce more light at a given voltage? (A) Increase the resistivity only. (B) Increase the diameter only. (C) Decrease the diameter only. (D) Decrease the diameter and increase the resistivity. (E) Increase the length only

(D) Dimensional analysis: 1.6 × 10^-3 A = 1.6 × 10^-3 C/s ÷ 1.6 × 10^-19 C/proton 10^16 protons/sec ÷10^9 protons/meter = 10^7 m/s

A narrow beam of protons produces a current of 1.6 × 10⁻³ A. There are 10⁹ protons in each meter along the beam. Of the following, which is the best estimate of the average speed of the protons in the beam? (A) 10⁻¹⁵ m/s (B) 10⁻¹² m/s (C) 10⁻⁷ m/s (D) 10⁷ m/s (E) 10¹² m/s

(B) Kirchhoff's loop rule (V = Q/C for a capacitor)

A resistor R and a capacitor C are connected in series to a battery of terminal voltage V0. Which of the following equations relating the current I in the circuit and the charge Q on the capacitor describes this circuit? (A) V₀²+QC-I²R=0 (B) V₀² - Q/C - IR = 0 (C) V₀²-Q²/2C-I²R=0 (D) V₀-CI-I²R=0 (E) Q/C-IR=0

(A) P = V2/R and if V is constant P ∝ 1/R

A variable resistor is connected across a constant voltage source. Which of the following graphs represents the power P dissipated by the resistor as a function of its resistance R?

(B) R = ρL/A. If L ÷ 2, R ÷ 2 and is r ÷ 2 then A ÷ 4 and R × 4 making the net effect R ÷ 2 × 4

A wire of length L and radius r has a resistance R. What is the resistance of a second wire made from the same material that has a length L/2 and a radius r/2? (A) 4R (B) 2R (C) R (D) R/2 (E) R/4

(D) P=I²R

A wire of resistance R dissipates power P when a current I passes through it. The wire is replaced by another wire with resistance 3R. The power dissipated by the new wire when the same current passes through it is (A) P/9 (B) P/3 (C) P (D) 3P (E) 6P

(D) P = IV = 1.56 kW. Energy = Pt = 1.56 kW × 8 h = 12.48 kW-h

An electric heater draws 13 amperes of current when connected to 120 volts. If the price of electricity is $0.10/kWh, what would be the approximate cost of running the heater for 8 hours? (A) $0.19 (B) $0.29 (C) $0.75 (D) $1.25 (E) $1.55

(D) With the switch closed, the resistance of the 15 Ω and the 30 Ω in parallel is 10 Ω, making the total circuit resistance 30 Ω and E = IR

An ideal battery, an ideal ammeter, a switch and three resistors are connected as shown. With the switch open as shown in the diagram the ammeter reads 2.0 amperes. When the switch is closed, what would be the current in the circuit? (A) 1.1 A (B) 1.7 A (C) 2.0 A (D) 2.3 A (E) 3.0 A

(D) ε = IR_total where R_total = 35 Ω

An ideal battery, an ideal ammeter, a switch and three resistors are connected as shown. With the switch open as shown in the diagram the ammeter reads 2.0 amperes. With the switch open, what must be the voltage supplied by the battery? (A) 30 V (B) 40 V (C) 60 V (D) 70 V (E) 110 V

(A) V = IR

An ideal battery, an ideal ammeter, a switch and three resistors are connected as shown. With the switch open as shown in the diagram the ammeter reads 2.0 amperes. With the switch open, what would be the potential difference across the 15 ohm resistor? (A) 30 V (B) 40 V (C) 60 V (D) 70 V (E) 110V

(C) 1 year = 365 days × 24 hours/day = 8760 hours. W (energy) = Pt = 0.1 kW × 8760 hours = 867 kW-h × $0.10 per kW-h = $ 86.7

Approximately how much would it cost to keep a 100 W light bulb lit continuously for 1 year at a rate of $0.10 per kW ⋅ hr? (A) $1 (B) $10 (C) $100 (D) $1000 (E) $100000

(A) When the switch is closed, the circuit behaves as if the capacitor were just a wire and all the potential of the battery is across the resistor. As the capacitor charges, the voltage changes over to the capacitor over time, eventually making the current (and the potential difference across the resistor) zero and the potential difference across the capacitor equal to the emf of the battery.

Assume the capacitor C is initially uncharged. The following graphs may represent different quantities related to the circuit as functions of time t after the switch S is closed Which graph best represents the current versus time in the circuit? (A) A (B) B (C) C (D) D (E) E

(B) When the switch is closed, the circuit behaves as if the capacitor were just a wire and all the potential of the battery is across the resistor. As the capacitor charges, the voltage changes over to the capacitor over time, eventually making the current (and the potential difference across the resistor) zero and the potential difference across the capacitor equal to the emf of the battery.

Assume the capacitor C is initially uncharged. The following graphs may represent different quantities related to the circuit as functions of time t after the switch S is closed Which graph best represents the voltage across the capacitor versus time? (A) A (B) B (C) C (D) D (E) E

(A) When the switch is closed, the circuit behaves as if the capacitor were just a wire and all the potential of the battery is across the resistor. As the capacitor charges, the voltage changes over to the capacitor over time, eventually making the current (and the potential difference across the resistor) zero and the potential difference across the capacitor equal to the emf of the battery.

Assume the capacitor C is initially uncharged. The following graphs may represent different quantities related to the circuit as functions of time t after the switch S is closed. Which graph best represents the voltage versus time across the resistor R? (A) A (B) B (C) C (D) D (E) E

(E) Since these resistors are in series, they must have the same current.

Two resistors of the same length, both made of the same material, are connected in a series to a battery as shown above. Resistor II has a greater cross. sectional area than resistor I. Which of the following quantities has the same value for each resistor? (A) Potential difference between the two ends (B) Electric field strength within the resistor (C) Resistance (D) Current per unit area (E) Current

(D) In series, the equivalent capacitance is calculated using reciprocals, like resistors in parallel. This results in an equivalent capacitance smaller than the smallest capacitor.

When two identical parallel-plate capacitors are connected in series, which of the following is true of the equivalent capacitance? (A) It depends on the charge on each capacitor. (B) It depends on the potential difference across both capacitors. (C) It is larger than the capacitance of each capacitor. (D) It is smaller than the capacitance of each capacitor. (E) It is the same as the capacitance of each capacitor.

(A) The equivalent resistance in parallel is smaller than the smallest resistance

When two resistors, having resistance R1 and R2, are connected in parallel, the equivalent resistance of the combination is 5 Ω. Which of the following statements about the resistances is correct? (A) Both R1 and R2, are greater than 5Ω (B) Both R1 and R2 are equal to 5 Ω (C) Both R1 and R2 are less than 5 Ω (D) The sum of R1 and R2 is 5 Ω (E) One of the resistances is greater than 5 Ω, one of the resistances is less than 5 Ω.

(E) To dissipate 24 W means R = V²/P = 6 Ω. The resistances, in order, are: 8 Ω, 4/3 Ω, 8/3 Ω, 12 Ω and 6 Ω

Which of the following combinations of 4Ω resistors would dissipate 24 W when connected to a 12 Volt battery?

(A) If the resistances are equal, they will all draw the same current

Which of the following statements is NOT true concerning the simple circuit shown where resistors R1, R2 and R3 all have equal resistances? (A) the largest current will pass through R1 (B) the voltage across R2 is 5 volts (C) the power dissipated in R3 could be 10 watts (D) if R2 were to burn out, current would still flow through both R1 and R3 (E) the net resistance of the circuit is less than R1

(D) Each computer draws I = P/V = 4.17 A. 4 computers will draw 16.7 A, while 5 will draw over 20 A.

Each member of a family of six owns a computer rated at 500 watts in a 120 V circuit. If all computers are plugged into a single circuit protected by a 20 ampere fuse, what is the maximum number of the computers can be operating at the same time? (A) 1 (B) 2 (C) 3 (D) 4 (E) 5 or more

(B) Resistance of bulbs B & C = 20 Ω combined with D in parallel gives 6.7 Ω for the right side. Combined with A & E in series gives a total resistance of 26.7 Ω. E = IR

Five identical light bulbs, each with a resistance of 10 ohms, are connected in a simple electrical circuit with a switch and a 10 volt battery as shown in the diagram below. The steady current in the above circuit would be closest to which of the following values? (A) 0.2 amp (B) 0.37 amp (C) 0.5 amp (D) 2.0 amp (E) 5.0 amp

(A) A and E failing in the main branch would cause the entire circuit to fail. B and C would affect each other.

Five identical light bulbs, each with a resistance of 10 ohms, are connected in a simple electrical circuit with a switch and a 10 volt battery as shown in the diagram below. Which bulb (or bulbs) could burn out without causing other bulbs in the circuit to also go out? (A) only bulb D (B) only bulb E (C) only bulbs A or E (D) only bulbs C or D (E) bulbs B, C, or D

(C) Shorting bulb 3 decreases the resistance in the right branch, increasing the current through bulb 4 and decreasing the total circuit resistance. This increases the total current in the main branch containing bulb 1.

For the circuit shown, a shorting wire of negligible resistance is added to the circuit between points A and B. When this shorting wire is added, bulb #3 goes out. Which bulbs (all identical) in the circuit brighten? (A) Only Bulb 2 (B) Only Bulb 4 (C) Only Bulbs 1 and 4 (D) Only Bulbs 2 and 4 (E) Bulbs 1, 2 and 4

(C) Wire CD shorts out bulb #3 so it will never light. Closing the switch merely adds bulb #2 in parallel to bulb #1, which does not change the potential difference across bulb #1

For the circuit shown, the ammeter reading is initially I. The switch in the circuit then is closed. Consequently: (A) The ammeter reading decreases. (B) The potential difference between E and F increases. (C) The potential difference between E and F stays the same. (D) Bulb #3 lights up more brightly. (E) The power supplied by the battery decreases.

(D) Shorting bulb 4 decreases the resistance in the right branch, increasing the current through bulb 3 and in the main branch containing bulb 1.

For the circuit shown, when a shorting wire (no resistance) connects the points labeled A and B, which of the numbered light bulbs become brighter? Assume that all four bulbs are identical and have resistance R . (A) Bulb 1 only (B) Bulb 2 only (C) Bulb 3 only (D) Bulbs 1 and 3 only (E) Bulbs 1, 2, and 3

(E) The total charge to be distributed is +100 µC - 50 µC = + 50 µC. In parallel, the capacitors must have the same voltage so the 20 µF capacitor has four times the charge of the 5 µF capacitor. This gives Q20 = 4Q5 and Q20 + Q5 = 4Q5 + Q5 = 5Q5 = 50 µC, or Q5 = 10 µC

For the configuration of capacitors shown, both switches are closed simultaneously. After equilibrium is established, what is the charge on the top plate of the 5 µF capacitor? (A) 100 µC (B) 50 µC (C) 30 µC (D) 25 µC (E) 10 µC

(E) If K burns out, the circuit becomes a series circuit with the three resistors, N, M and L all in series, reducing the current through bulb N.

Four identical light bulbs K, L, M, and N are connected in the electrical circuit shown above. Bulb K burns out. Which of the following statements is true? (A) All the light bulbs go out. (B) Only bulb N goes out. (C) Bulb N becomes brighter. (D) The brightness of bulb N remains the same. (E) Bulb N becomes dimmer but does not go out.

(E) If M burns out, the circuit becomes a series circuit with the two resistors, N and K in series, with bulb L going out as well since it is in series with bulb M.

Four identical light bulbs K, L, M, and N are connected in the electrical circuit shown above. Bulb M burns out. Which of the following statements is true? (A) All the light bulbs go out. (B) Only bulb M goes out. (C) Bulb N goes out but at least one other bulb remains lit. (D) The brightness of bulb N remains the same. (E) Bulb N becomes dimmer but does not go out.

(D) N is in the main branch, with the most current. The current then divides into the two branches, with K receiving twice the current as L and M. The L/M branch has twice the resistance of the K branch. L and M in series have the same current. Current is related to brightness (P = I²R)

Four identical light bulbs K, L, M, and N are connected in the electrical circuit shown above. In order of decreasing brightness (starting with the brightest), the bulbs are: (A) K = L > M > N (B) K = L = M > N (C) K > L = M > N (D) N > K > L = M (E) N > K = L = M

(D) N is in the main branch, with the most current. The current then divides into the two branches, with K receiving twice the current as L and M. The L/M branch has twice the resistance of the K branch. L and M in series have the same current

Four identical light bulbs K, L, M, and N are connected in the electrical circuit shown above. Rank the current through the bulbs. (A) K > L > M > N (B) L = M > K = N (C) L > M > K > N (D) N > K > L = M (E) N > L = M > K

(C) For the currents in the branches to be equal, each branch must have the same resistance

Given the simple electrical circuit above, if the current in all three resistors is equal, which of the following statements must be true? (A) X, Y, and Z all have equal resistance (B) X and Y have equal resistance (C) X and Y added together have the same resistance as Z (D) X and Y each have more resistance than Z (D) none of the above must be true

(E) The equivalent resistance of the two 4 Ω resistors on the right is 2 Ω making the total circuit resistance 10 Ω and the total current 2.4 A. The 2.4 A will divide equally between the two branches on the right. Q = It = (1.2 A)(5 s) = 6 C

How many coulombs will pass through the identified resistor in 5 seconds once the circuit was closed? (A) 1.2 (B) 12 (C) 2.4 (D) 24 (E) 6

(B) P = I²R

How much current flows through a 4 ohm resistor that is dissipating 36 watts of power? (A) 2.25 amps (B) 3.0 amps (C) 4.24 amps (D) 9.0 amps (E) 144 amps

(D) Resistor D is in a branch by itself while resistors A, B and C are in series, drawing less current than resistor D.

If all of the resistors in the above simple circuit have the same resistance, which would dissipate the greatest power? (A) resistor A (B) resistor B (C) resistor C (D) resistor D (E) they would all dissipate the same power

(E) For the ammeter to read zero means the junctions at the ends of the ammeter have the same potential. For this to be true, the potential drops across the 1 Ω and the 2 Ω resistor must be equal, which means the current through the 1 Ω resistor must be twice that of the 2 Ω resistor. This means the resistance of the upper branch (1 Ω and 3 Ω) must be ½ that of the lower branch (2 Ω and R) giving 1 Ω + 3 Ω = ½ (2 Ω + R)

If the ammeter in the circuit above reads zero, what is the resistance R ? (A) 1.5 Ω (B) 2Ω (C) 4 Ω (D) 5 Ω (E) 6Ω

(A) R = V/I where V = W/Q and Q = It giving R = W/I²t and W = joules = kg m²/s²

In terms of the seven fundamental SI units in the MKS system, the Ohm is written as In terms of the seven fundamental SI units in the MKS system, the Ohm is written as (A) (kg*m²)/(A²*s³) (B) (kg*m²*s)/(C²) (C) (kg*m)/(C*s) (D) (kg*m²)/(A*s²) (E) (kg*s²)/(A²*m²)

(D) If the current in the 6 Ω resistor is 1 A, then by ratios, the currents in the 2 Ω and 3 Ω resistor are 3 A and 2 A respectively (since they have 1/3 and 1/2 the resistance). This makes the total current 6 A and the potential drop across the 4 Ω resistor 24 V. Now use Kirchhoff's loop rule for any branch.

In the accompanying circuit diagram, the current through the 6.0-Ω resistor is 1.0 A. What is the power supply voltage V? (A) 10 V (B) 18 V (C) 24 V (D) 30 V (E) 42 V

(C) With a total resistance of 10 Ω, the total current is 1.2 A. The terminal voltage V_T = ε- Ir

In the circuit above the voltmeter V draws negligible current and the internal resistance of the battery is 1.0 ohm. The reading of the voltmeter is (A) 10.5 V (B) 12.0 V (C) 10.8 V (D) 13.0 V (E) 11.6 V

(C) Summing the potential differences: - 6 V - (2 A)(0.2 Ω) - (2A)(1 Ω) = - 8.4 V

In the circuit above, the emf's and the resistances have the values shown. The current I in the circuit is 2 amperes. The potential difference between points X and Y is (A) 1.2 V (B) 6.0 V (C) 8.4 V (D) 10.8 V (E) 12.2 V

(C) Energy = Pt = I²Rt

In the circuit above, the emf's and the resistances have the values shown. The current I in the circuit is 2 amperes. How much energy is dissipated by the 1.5-ohm resistor in 60 seconds? (A) 6 J (B) 180 J (C) 360 J (D) 720 J (E) 1,440 J

(A) Utilizing Kirchhoff's loop rule starting at the upper left and moving clockwise: - (2 A)(0.3 Ω) + 12 V - 6 V - (2 A)(0.2 Ω) -(2A)(R) - (2A)(1.5 Ω) = 0

In the circuit above, the emf's and the resistances have the values shown. The current I in the circuit is 2 amperes. The resistance R is (A) 1 Ω (B) 2Ω (C) 3 Ω (D) 4 Ω (E) 6 Ω

(C) Bulb C in the main branch receiving the total current will be the brightest

In the circuit diagram above, all of the bulbs are identical. Which bulb will be the brightest? (A) A (B) B (C) C (D) D (E) The bulbs all have the same brightness.

(C) The voltage across the capacitor is 6 V (Q = CV) and since the capacitor is in parallel with the 300 Ω resistor, the voltage across the 300 Ω resistor is also 6 V. The 200 Ω resistor is not considered since the capacitor is charged and no current flows through that branch. The 100 Ω resistor in series with the 300 Ω resistor has 1/3 the voltage (2 V) since it is 1/3 the resistance. Kirchhoff's loop rule for the left loop gives E = 8 V.

In the circuit diagrammed above, the 3.00-µF capacitor is fully charged at 18.0 µC. What is the value of the power supply voltage V? (A) 4.40 V (B) 6.00 V (C) 8.00 V (D) 10.4 V (E) 11.0 V

(A) When the capacitor is fully charged, the branch with the capacitor is "closed" to current, effectively removing it from the circuit for current analysis

In the circuit shown above, the battery supplies a constant voltage V when the switch S is closed. The value of the capacitance is C, and the value of the resistances are R1 and R2. A long time after the switch has been closed, the current supplied by the battery is (A) V/(R1 + R2) (B) V/R1 (C) V/R2 (D) V(R1 + R2)/R1R2 (E) zero

(B) When the switch is closed, the circuit behaves as if the capacitor were just a wire, shorting out the resistor on the right.

In the circuit shown above, the battery supplies a constant voltage V when the switch S is closed. The value of the capacitance is C, and the value of the resistances are R1 and R2. Immediately after the switch is closed, the current supplied by the battery is (A) V/(R1 + R2) (B) V/R1 (C) V/R2 (D) V(R1 + R2)/R1R2 (E) zero

(D) The equivalent resistance of the 20 Ω and the 60 Ω in parallel is 15 Ω, added to the 35 Ω resistor in series gives 15 Ω + 35 Ω = 50 Ω

In the circuit shown above, the equivalent resistance of the three resistors is (A) 10.5 Ω (B) 15Ω (C) 20 Ω (D) 50 Ω (E) 115 Ω

(A) For points a and b to be at the same potential, the potential drop across the 3 Ω resistor must be equal to the potential drop across capacitor C. The potential drop across the 3 Ω resistor is three times the drop across the 1 Ω resistor. For the potential drop across capacitor C to be three times the crop across the 1 µF capacitor, C must be 1/3 the capacitance, or 1/3 µF

In the circuit shown above, the potential difference between points a and b is zero for a value of capacitance C of (A) 1/3 microfarad (B) 2/3 microfarad (C) 2 microfarads (D) 3 microfarads (E) 9 microfarads

(C) When the capacitor is fully charged, the branch on the right has no current, effectively making the circuit a series circuit with the 100 Ω and 300 Ω resistors. Rtotal= 400 Ω, E = 10 V = IR

See the accompanying figure. What is the current through the 300 Ω resistor when the capacitor is fully charged? (A) zero (B) 0.020 A (C) 0.025 A (D) 0.033 A (E) 0.100 A

(E) Most rapid heating requires the largest power dissipation. This occurs with the resistors in parallel.

Suppose you are given a constant voltage source V0 and three resistors R1, R2, and R3 with R1 > R2 > R3. If you wish to heat water in a pail which of the following combinations of resistors will give the most rapid heating?

(B) Since the 5 µF capacitor is in parallel with the battery, the potential difference across it is 100 V. Q = CV

The charge stored in the 5-microfarad capacitor is most nearly (A) 360 µC (B) 500 µC (C) 710 µC (D) 1,100 µC (E) 1,800 µC

(B) Closing the switch short circuits Bulb 2 causing no current to flow to it. Since the bulbs were originally in series, this decreases the total resistance and increases the total current, making bulb 1 brighter

The circuit in the figure above contains two identical lightbulbs in series with a battery. At first both bulbs glow with equal brightness. When switch S is closed, which of the following occurs to the bulbs? Bulb I | Bulb 2 (A) Goes out | Gets brighter (B) Gets brighter | Goes out (C) Gets brighter | Gets slightly dimmer (D) Gets slightly dimmer | Gets brighter (E) Nothing | Goes out

(D) For steady power dissipation, the circuit must allow current to slow indefinitely. For the greatest power, the total resistance should be the smallest value. These criteria are met with the resistors in parallel.

The five incomplete circuits below are composed of resistors R, all of equal resistance, and capacitors C, all of equal capacitance. A battery that can be used to complete any of the circuits is available. Into which circuit should the battery be connected to obtain the greatest steady power dissipation? (A) A (B) B (C) C (D) D (E) E

(B) To retain energy, there must be a capacitor that will not discharge through a resistor. Capacitors in circuits C and E will discharge through the resistors in parallel with them

The five incomplete circuits below are composed of resistors R, all of equal resistance, and capacitors C, all of equal capacitance. A battery that can be used to complete any of the circuits is available. Which circuit will retain stored energy if the battery is connected to it and then disconnected? (A) A (B) B (C) C (D) D (E) E

(B) R = ρL/A. Greatest resistance is the longest, narrowest resistor.

The five resistors shown below have the lengths and cross-sectional areas indicated and are made of material with the same resistivity. Which has the greatest resistance?

(E) R = ρL/A. Least resistance is the widest, shortest resistor

The five resistors shown below have the lengths and cross-sectional areas indicated and are made of material with the same resistivity. Which resistor has the least resistance?

(E) Even though the wires have different resistances and currents, the potential drop across each is 1.56 V and will vary by the same gradient, dropping all 1.56 V along the same length.

The following diagram represents an electrical circuit containing two uniform resistance wires connected to a single flashlight cell. Both wires have the same length, but the thickness of wire X is twice that of wire Y. Which of the following would best represent the dependence of electric potential on position along the length of the two wires?

(C) P = I²R and R = ρL/A giving P ∝ ρL/d²

The power dissipated in a wire carrying a constant electric current I may be written as a function of the length l of the wire, the diameter d of the wire, and the resistivity ρ of the material in the wire. In this expression, the power dissipated is directly proportional to which of the following? (A) l only (B) d only (C) l and ρ only (D) d and ρ only (E) l, d, and ρ

(A) By process of elimination, A is the only possible true statement

The total capacitance of several capacitors in parallel is the sum of the individual capacitance's for which of the following reasons? (A) The charge on each capacitor depends on its capacitance, but the potential difference across each is the same. (B) The charge is the same on each capacitor, but the potential difference across each capacitor depends on its capacitance. (C) Equivalent capacitance is always greater than the largest capacitance. (D) Capacitors in a circuit always combine like resistors in series. (E) The parallel combination increases the effective separation of the plates.

(D) Using Kirchhoff's loop rule around the circuit going through either V or R since they are in parallel and will have the same potential drop gives: - V - (1.00 mA)(25 Ω) + 5.00 V - (1.00mA)(975 Ω) = 0

The voltmeter in the accompanying circuit diagram has internal resistance 10.0 kΩ and the ammeter has internal resistance 25.0 Ω. The ammeter reading is 1.00 mA. The voltmeter reading is most nearly: (A) 1.0 V (B) 2.0 V (C) 3.0 V (D) 4.0 V (E) 5.0 V

(E) In series 1/C_T = ∑1/C

Three 1/2 μF capacitors are connected in series as shown in the diagram above. The capacitance of the combination is (A) 0.1 μF (B) 1 μF (C) 2/3 μF (D) ½ μF (E) 1/6 μF

(C) There are several ways to do this problem. We can find the total energy stored and divide it into the three capacitors: U_C = ½ CV² = ½ (2 µF)(6 V)²= 36 µJ ÷ 3 = 12 µJ each

Three 6-microfarad capacitors are connected in series with a 6-volt battery. The energy stored in each capacitor is (A) 4 µJ (B) 6 µJ (C) 12 µJ (D) 18 µJ (E) 36 µJ

(B) In series 1/C_T = ∑1/C

Three 6-microfarad capacitors are connected in series with a 6-volt battery. The equivalent capacitance of the set of capacitors is (A) 0.5 µF (B) 2 µF (C) 3 µF (D) 9 µF (E) 18 µF

(D) In parallel, all the resistors have the same voltage (2 V). P3 = I3V3

Three different resistors R1, R2 and R3 are connected in parallel to a battery. Suppose R1 has 2 V across it, R2 = 4 Ω, and R3 dissipates 6 W. What is the current in R3? (A) 0.33 A (B) 0.5 A (C) 2 A (D) 3 A (E) 12 A

(B) The capacitance of the two capacitors in parallel is 2C. Combined with a capacitor in series gives C = (C*2C)/(C+2C) = 2/3C

Three identical capacitors each with a capacitance of C are connected as shown in the following diagram. What would be the total equivalent capacitance of the circuit? (A) 0.33 C (B) 0.67 C (C) 1.0 C (D) 1.5 C (E) 3.0 C

(B) The equivalent capacitance of the two 3 µF capacitors in parallel is 6 µF, combined with the 3 µF in series gives Ctotal= 2 µF

Three identical capacitors, each of capacitance 3.0 µF, are connected in a circuit with a 12 V battery as shown above. The equivalent capacitance between points X and Z is (A) 1.0 µF (B) 2.0 µF (C) 4.5 µF (D) 6.0 µF (E) 9.0 µF

(D) The equivalent capacitance between X and Y is twice the capacitance between Y and Z. Thismeans the voltage between X and Y is ½ the voltage between Y and Z. For a total of 12 V, this gives 4 V between X and Y and 8 V between Y and Z.

Three identical capacitors, each of capacitance 3.0 µF, are connected in a circuit with a 12 V battery as shown above. The potential difference between points Y and Z is (A) zero (B) 3 V (C) 4 V (D) 8 V (E) 9 V

(C) In series, they all have the same current, 2 A. P3 = I3V3

Three resistors - R1, R2, and R3 - are connected in series to a battery. Suppose R1 carries a current of 2.0 A, R2 has a resistance of 3.0 Ω, and R3 dissipates 6.0 W of power. What is the voltage across R3? (A) 1.0 V (B) 2.0 V (C) 3.0 V (D) 6.0 V (E) 12 V

(D) In parallel V1 = V2. Q1 = C1V1 and Q2 = C2V2 so Q1/Q2 = C1/C2 = 1.5

Two capacitors are connected in parallel as shown above. A voltage V is applied to the pair. What is the ratio of charge stored on C₁ to the charge stored on C₂, when C₁ = 1.5C₂ ? (A) 4/9 (B) 2/3 (C) 1 (D) 3/2 (E) 9/4

(D) The larger loop, with twice the radius, has twice the circumference (length) and R = ρL/A

Two concentric circular loops of radii b and 2b, made of the same type of wire, lie in the plane of the page, as shown above. The total resistance of the wire loop of radius b is R. What is the resistance of the wire loop of radius 2b? (A) R/4 (B) R/2 (C) R (D) 2R (E) 4R

(B) R = ρL/A ∝ L/d2 where d is the diameter. Rx/Ry = Lx/dx² ÷ Ly/dy²= (2Ly)dy²/[Ly(2dy)]² = ½

Two conducting cylindrical wires are made out of the same material. Wire X has twice the length and twice the diameter of wire Y. What is the ratio Rx/Ry (A) 1/4 (B) ½ (C) 1 (D) 2 (E) 4

(C) R = ρL/A ∝ L/d2 where d is the diameter. R_II/R_I =L_II/d_II² ÷ L_I/d_I² = (2L_I)d_I²/[L_I(2d_I)2] = ½

Wire I and wire II are made of the same material. Wire II has twice the diameter and twice the length of wire I. If wire I has resistance R, wire II has resistance (A) R/8 (B) R/4 (C) R/2 (D) R (E) 2R

(A) R ∝ L/A = L/d². If d × 2, R ÷ 4 and if L ÷ 2, R ÷ 2 making the net effect R ÷ 8

Wire Y is made of the same material but has twice the diameter and half the length of wire X. If wire X has a resistance of R then wire Y would have a resistance of (A) R/8 (B) R/2 (C) R (D) 2R (E) 8R

(C) Using all three in series = 3 Ω, all three in parallel = 1/3 Ω. One in parallel with two in series = 2/3 Ω, one in series with two in parallel = 3/2 Ω

You are given three 1.0 Ω resistors. Which of the following equivalent resistances CANNOT be produced using all three resistors? (A) 1/3 Ω (B) 2/3 Ω (C) 1.0 Ω (D) 1.5 Ω (E) 3.0 Ω

(C) Total resistance = E/I = 25 Ω. Resistance of the 30 Ω and 60 Ω resistors in parallel = 20 Ω adding the internal resistance in series with the external circuit gives Rtotal= 20 Ω + r = 25 Ω

A 30-ohm resistor and a 60-ohm resistor are connected as shown above to a battery of emf 20 volts and internal resistance r. The current in the circuit is 0.8 ampere. What is the value of r? (A) 0.22 Ω (B) 4.5 Ω (C) 5 Ω (D) 16Ω (E) 70 Ω

(E) Since the volume of material drawn into a new shape in unchanged, when the length is doubled, the area is halved. R = ρL/A

A cylindrical resistor has length L and radius r. This piece of material is then drawn so that it is a cylinder with new length 2L. What happens to the resistance of this material because of this process? (A) the resistance is quartered. (B) the resistance is halved. (C) the resistance is unchanged. (D) the resistance is doubled. (E) the resistance is quadrupled.

(D) Total circuit resistance of the load = R/2. Total circuit resistance including the internal resistance = r + R/2. The current is then E/(r + R/2) and the total power dissipated in the load is P = I2R_load= (ε²R/2)/(r + R/2)². Using calculus max/min methods or plotting this on a graph gives the value of R for which this equation is maximized of R = 2r. This max/min problem is not part of the B curriculum but you should be able to set up the equation to be maximized

A battery having emf E and internal resistance r is connected to a load consisting of two parallel resistors each having resistance R. At what value of R will the power dissipated in the load be a maximum? (A) 0 (B) r/2 (C) r (D) 2r (E) 4r

(A) Closing the switch reduces the total resistance of the circuit, increasing the current in the main branch containing bulb 1

A circuit is connected as shown. All light bulbs are identical. When the switch in the circuit is closed illuminating bulb #4, which other bulb(s) also become brighter? (A) Bulb #1 only (B) Bulb #2 only (C) Bulbs #2 and #3 only (D) Bulbs #1, #2, and #3 (E) None of the bulbs.

(B) In series circuits, larger resistors develop more power

A current through the thin filament wire of a light bulb causes the filament to become white hot, while the larger wires connected to the light bulb remain much cooler. This happens because (A) the larger connecting wires have more resistance than the filament. (B) the thin filament has more resistance than the larger connecting wires. (C) the filament wire is not insulated. (D) the current in the filament is greater than that through the connecting wires. (E) the current in the filament is less than that through the connecting wires.

(C) Resistivity is dependent on the material. Not to be confused with resistance

A cylindrical graphite resistor has length L and cross-sectional area A. It is to be placed into a circuit, but it first must be cut in half so that the new length is ½ L. What is the ratio of the new resistivity to the old resistivity of the cylindrical resistor? (A) 4 (B) 2 (C) 1 (D) ½ (E) ¼

(C) Each branch, with two capacitors in series, has an equivalent capacitance of 2 µF ÷ 2 = 1 µF. The three branches in parallel have an equivalent capacitance of 1 µF + 1 µF + 1 µF = 3 µF

Below is a system of six 2-microfarad capacitors. The equivalent capacitance of the system of capacitors is (A) 2/3µF (B) 4/3 µF (C) 3 µF (D) 6 µF (E) 12 µF

(C) For each capacitor to have 6 µC, each branch will have 6 µC since the two capacitors in series in each branch has the same charge. The total charge for the three branches is then 18 µC. Q = CV gives 18 µC = (3 µF)V

Below is a system of six 2-microfarad capacitors. What potential difference must be applied between points X and Y so that the charge on each plate of each capacitor will have magnitude 6 microcoulombs? (A) 1.5 V (B) 3V (C) 6 V (D) 9 V (E) 18 V

(C) If A were to burn out, the total resistance of the parallel part of the circuit increases, causing less current from the battery and less current through bulb A. However, A and B split the voltage from the battery in a loop and with less current through bulb A, A will have a smaller share of voltage, increasing the potential difference (and the current) through bulb B.

Consider a simple circuit containing a battery and three light bulbs. Bulb A is wired in parallel with bulb B and this combination is wired in series with bulb C. What would happen to the brightness of the other two bulbs if bulb A were to burn out? (A) There would be no change in the brightness of either bulb B or bulb C. (B) Both would get brighter. (C) Bulb B would get brighter and bulb C would get dimmer. (D) Bulb B would get dimmer and bulb C would get brighter. (E) Only bulb B would get brighter

(E) The current through bulb 3 is twice the current through 1 and 2 since the branch with bulb 3 is half the resistance of the upper branch. The potential difference is the same across each branch, but bulbs 1 and 2 must divide the potential difference between them.

Consider the compound circuit shown above. The three bulbs 1, 2, and 3 - represented as resistors in the diagram - are identical. Which of the following statements are true? I. Bulb 3 is brighter than bulb 1 or 2. II. Bulb 3 has more current passing through it than bulb 1 or 2. III. Bulb 3 has a greater voltage drop across it than bulb 1 or 2. (A) I only (B) II only (C) I & II only (D) I & III only (E) I, II, & III

(A) Breaking the circuit in the lower branch lowers the total current in the circuit, decreasing the voltage across R1. Looking at the upper loop, this means R2 now has a larger share of the battery voltage and the voltage across AD is the same as the voltage across BC

The circuit shown has an ideal ammeter with zero resistance and four identical resistance light bulbs which are initially illuminated. A person removes the bulb R4 from its socket thereby permanently breaking the electrical circuit at that point. Which statement is true of the circuit after removing the bulb? (A) The voltage from B → C increases. (B) The power supplied by the battery increases (C) The voltage across R1 (D) The ammeter reading is unchanged. increases. (E) The bulb R2 maintains the same brightness

(D) Bulbs in the main branch have the most current through them and are the brightest.

The diagram above represents a simple electric circuit composed of 5 identical light bulbs and 2 flashlight cells. Which bulb (or bulbs) would you expect to be the brightest? (A) V only (B) V and W only (C) V and Z only (D) V, W and Z only (E) all five bulbs are the same brightness

(D) Resistors J and N are in the main branch and therefore receive the largest current

The diagram below shows five identical resistors connected in a combination series and parallel circuit to a voltage source. Through which resistor(s) would there be the greatest current? (A) J only (B) M only (C) N only (D) J&N only (E) K&L only

(D) P = I²R

The diagram below shows five identical resistors connected in a combination series and parallel circuit to a voltage source. Which resistor(s) have the greatest rate of energy dissipation? (A) J only (B) M only (C) N only (D) J&N only (E) K&L only

(D) The capacitance of the 4 µF and 2µF in parallel is 6 µF. Combined with the 3µF in series gives 2 µF for the right branch. Added to the 5 µF in parallel gives a total of 7 µF

The equivalent capacitance for this network is most nearly (A) 10/7 µF (B) 3/2 µF (C) 7/3 µF (D) 7 µF (E) 14 µF

(B) In parallel 1/R_t = ∑ 1/R

The equivalent resistance of the circuit shown to the right with resistances R1 = 4.00 Ω, R2 = 3.00 Ω, and R3 = 2.00 Ω is (A) 0.111 Ω (B) 0.923 Ω (C) 1.08 Ω (D) 3.00 Ω (E) 9.00 Ω

(C) Summing the potential differences from bottom to top: left circuit: - (1 A)r + E = 10 V right circuit: + (1 A)r + E = 20 V, solve simultaneous equations

The figures above show parts of two circuits, each containing a battery of emf ε and internal resistance r. The current in each battery is 1 A, but the direction of the current in one battery is opposite to that in the other. If the potential differences across the batteries' terminals are 10 V and 20 V as shown, what are the values of ε and r ? (A) E = 5 V, r = 15 Ω (B) E =10 V, r = 100 Ω (C) E = 15 V, r = 5 Ω (D) E = 20 V, r = 10 Ω (E) The values cannot be computed unless the complete circuits are shown.

(A) If you perform Kirchhoff's loop rule for the highlighted loop, you get a current of 0 A through the 6 Ω resistor.

What is the current through the 6.0 Ω resistor shown in the accompanying circuit diagram? Assume all batteries have negligible resistance. (A) 0 (B) 0.40 A (C) 0.50 A (D) 1.3 A (E) 1.5 A

(D) P = V²/R

What is the resistance of a 60 watt light bulb designed to operate at 120 volts? (A) 0.5 Ω (B) 2 Ω (C) 60 Ω (D) 240 Ω (E) 7200 Ω

(D) P = E²/R. Total resistance of n resistors in series is nR making the power P = E²/nR = P/n

When a single resistor is connected to a battery, a total power P is dissipated in the circuit. How much total power is dissipated in a circuit if n identical resistors are connected in series using the same battery? Assume the internal resistance of the battery is zero. (A) n²P (B) nP (C) P (D) P/n (E) P/n²

(E) by definition of a parallel circuit

When any four resistors are connected in parallel, the _______ each resistor is the same. (A) charge on (B) current through (C) power from (D) resistance of (E) voltage across

(B) Closing the switch reduces the resistance in the right side from 20 Ω to 15 Ω, making the total circuit resistance decrease from 35 Ω to 30 Ω, a slight decrease, causing a slight increase in current. For the current to double, the total resistance must be cut in half.

When the switch S is open in the circuit shown above, the reading on the ammeter A is 2.0 A. When the switch is closed, the reading on the ammeter is (A) doubled (B) increased slightly but not doubled (C) the same (D) decreased slightly but not halved (E) halved