Revised Circuits

(D) 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? (CHOICE E REPLACES CHOICE D)

(A) Current is greatest where resistance is least. The resistances are, in order, 1 Ω, 2 Ω, 4 Ω, 2 Ω and 6 Ω

The batteries in each of the circuits shown above are identical and the wires have negligible resistance. (IGNORE OPTION E) In which circuit is the current furnished by the battery the greatest (A) A (B) B (C) C (D) D

(D) Current is greatest where resistance is least. The resistances are, in order, 1 Ω, 2 Ω, 4 Ω, 2 Ω and 6 Ω.

The batteries in each of the circuits shown above are identical and the wires have negligible resistance. (OPTION E REPLACES D) In which circuit is the equivalent resistance connected to the battery the greatest? (A) A (B) B (C) C (D) D

(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

(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 (C) 2R (D) 8R

(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

(D) 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 doubled. (D) the resistance is quadrupled.

(B) P = V²/R and R = ρL/A giving P = V²A/ρL

A fixed voltage is applied across the length of a tungsten wire. An increase in the power dissipated by the wire would result if which of the following could be increased? (A) The resistivity of the tungsten (B) The cross-sectional area of the wire (C) The length of the wire (D) The temperature of the wire

(A) Starting at A and summing potential differences counterclockwise to point C gives 12 V

An electric circuit consists of a 12 V battery, an ideal 10 A fuse, and three 2 Ω resistors connected as shown above What would be the reading on a voltmeter connected across points A and C ? (A) 12 V (B) 6 V (C) 3 V (D) 2 V

(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

(D) The resistance of the two resistors in parallel is r/2. The total circuit resistance is then 10 Ω + ½r, which is equivalent to ε/I = (10 V)/(0.5 A) = 20 Ω = 10 Ω + r/2

In the circuit shown above, the value of r for which the current I is 0.5 ampere is (A) 1 Ω (B) 5 Ω (C) 10 Ω (D) 20 Ω

(C) The 15 Ω resistor would be in parallel with the 30 Ω resistor when the switch is closed.

A battery, an ammeter, three resistors, and a switch are connected to form the simple circuit shown above. When the switch is closed what would happen to the potential difference across the 15 ohm resistor? (A) it would equal the potential difference across the 20 ohm resistor (B) it would be twice the potential difference across the 30 ohm resistor (C) it would equal the potential difference across the 30 ohm resistor (D) it would be half the potential difference across the 30 ohm resistor

(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

(A) Adding resistors in parallel decreases the total circuit resistance, this increasing the total current in the circuit.

A lamp, a voltmeter V, an ammeter A, and a battery with zero internal resistance are connected as shown above. Connecting another lamp in parallel with the first lamp as shown by the dashed lines would (A) increase the ammeter reading (B) decrease the ammeter reading (C) increase the voltmeter reading (D) decrease the voltmeter reading (E) produce no change in either meter reading

(D) Before cutting the resistance is R. After cutting we have two wires of resistance ½ R which in parallel is an equivalent resistance of ¼ R. P = V²/R and I = V/R

A length of wire of resistance R is connected across a battery with zero internal resistance. The wire is then cut in half and the two halves are connected in parallel. When the combination is reconnected across the battery, what happens to the resultant power dissipated and the current drawn from the battery? Power Current (A) Doubles Doubles (B) Quadruples Doubles (C) Doubles Quadruples (D) Quadruples Quadruples

(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/4

(C) 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) 3P (D) 6P

(C) The branch with two 2 Ω resistors has a total resistance of 4 Ω and a potential difference of 12 V. V = IR

An electric circuit consists of a 12 V battery, an ideal 10 A fuse, and three 2 Ω resistors connected as shown above What would be the reading on an ammeter inserted at point B ? (A) 9 A (B) 6 A (C) 3 A (D) 2 A

(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

(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.

(C) 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 2 only (B) Bulb 3 only (C) Bulbs 1 and 3 only (D) Bulbs 1, 2, and 3

(C) 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) L = M > K = N (B) L > M > K > N (C) N > K > L = M (D) N > K = L = M

(C) 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) L = M > K = N (B) L > M > K > N (C) N > K > L = M (D) N > L = M > K

(A) The resistances are, respectively, 4/3 R, 2/5 R, R, and 5/3 R

Given 4 identical resistors of resistance R, which of the following circuits would have an equivalent resistance of 4/3 R?

(A) I1 is the main branch current and is the largest. It will split into I2 and I3 and since I2 moves through the smaller resistor, it will be larger than I3.

How do the currents I1, I2, and 13 compare? (A) I1 > I2 > I3 (B) I1 > I3 > I2 (C) I2 > I1 > I3 (D) I3 > I1 > I2

(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

(C) S1 must be closed to have any current. Closing S2 will allow current in R2 but closing R3 would short circuit R2

In the circuit above, the resistors all have the same resistance. The battery, wires, and ammeter have negligible resistance. A closed switch also has negligible resistance Closing which of the switches will produce the greatest power dissipation in R 2 ? (A) S 1 only (B) S 2 only (C) S 1 and S 2 only (D) S 1 and S 3 only

(D) Total circuit resistance (including internal resistance) = 40 Ω; total current = 0.3 A. ε = IR

The above circuit diagram shows a battery with an internal resistance of 4.0 ohms connected to a 16-ohm and a 20-ohm resistor in series. The current in the 20-ohm resistor is 0.3 amperes What is the emf of the battery? (A) 1.2 V (B) 6.0 V (C) 10.8 V (D) 12.0 V

(A) P = I²r

The above circuit diagram shows a battery with an internal resistance of 4.0 ohms connected to a 16-ohm and a 20-ohm resistor in series. The current in the 20-ohm resistor is 0.3 amperes What power is dissipated by the 4-ohm internal resistance of the battery? (A) 0.36 W (B) 1.2 W (C) 3.2 W (D) 3.6 W

(D) Least power is for the greatest resistance (P = ε²/R)

The batteries in each of the circuits shown above are identical and the wires have negligible resistance. (OPTION E REPLACES D) Which circuit dissipates the least power? (A) A (B) B (C) C (D) D

(B) P = Iε

The circuit shown above left is made up of a variable resistor and a battery with negligible internal resistance. A graph of the power P dissipated in the resistor as a function of the current I supplied by the battery is given above right. What is the emf of the battery? (A) 0.025 V (B) 2.5 V (C) 6.25 V (D) 40 V

(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

(A) Resistance of the 1 Ω and 3 Ω in series = 4 Ω. This, in parallel with the 2 Ω resistor gives (2 × 4) /(2 + 4) = 8/6 Ω. Also notice the equivalent resistance must be less than 2 Ω (the 2 Ω resistor is in parallel and the total resistance in parallel is smaller than the smallest resistor) and there is only one choice smaller than 2 Ω

The electrical resistance of the part of the circuit shown between point X and point Y is (A) 4/3 Ω (B) 2 Ω (C) 4 Ω (D) 6 Ω

(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?

(C) Closing the switch adds another parallel branch, increasing the total current delivered by the battery. Bulb 3 will get brighter. Bulb 2, in its own loop with bulb 3 and the battery will then lose some of its share of the potential difference from the battery and will get dimmer.

The three lightbulbs in the circuit above are identical, and the battery has zero internal resistance. When switch S is closed to cause bulb 1 to light, which of the other two bulbs increase(s) in brightness? (A) Neither bulb (B) Bulb 2 only (C) Bulb 3 only (D) Both bulbs

(C) 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) 0.5 A (B) 2 A (C) 3 A (D) 12 A

(B) 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) 3.0 V (C) 6.0 V (D) 12 V

(C) 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) 2R (E) 4R

(A)

What would be the current at point E in the circuit? (A) 2 amp (B) 4 amp (C) 5 amp (D) 7 amp

(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) decreased slightly but not halved (D) halved

(B) Voltmeters must be placed in parallel and ammeters must be placed in series.

Which of the following wiring diagrams could be used to experimentally determine R using Ohm's Law? Assume an ideal voltmeter and an ideal ammeter.

(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

(D) 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) four times as large (C) twice as large (D) equally as large

(C) 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) -3 V (D) -7 V

(A)

A 9-volt battery is connected to four resistors to form a simple circuit as shown below. What would be the potential at point B with respect to point D in the above circuit? (A) +2 V (B) +4 V (C) +5 V (D) +7 V

(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

(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

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

A student 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) Increase the length only

(C) 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) 2.0 A (C) 2.3 A (D) 3.0 A

(C) 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) 60 V (C) 70 V (D) 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) 60 V (C) 70 V (D) 110V

(B) W = Pt = I²Rt

An immersion heater of resistance R converts electrical energy into thermal energy that is transferred to the liquid in which the heater is immersed. If the current in the heater is I, the thermal energy transferred to the liquid in time t is (A) IRt (B) I²Rt (C) IRt² (D) IR/t

(C) With B2 burning out, the total resistance of the circuit increases as it is now a series circuit. This decreases the current in the main branch, decreasing V1. For V1 to be halved, the current must be halved which means the total resistance must be doubled, which by inspection did not happen in this case (total before = 5/3 R, total after = 3 R)

B1, B2, B3, and B4 are identical light bulbs. There are six voltmeters connected to the circuit as shown. All voltmeters are connected so that they display positive voltages. Assume that the voltmeters do not affect the circuit. If B 2 were to burn out, opening the circuit, what would happen to the reading of V 1 ? Let V be its original reading when all bulbs are functioning and let V be its reading when B 2 is burnt out. (A) V > 2V (B) 2V > V > V (C) V > V > V/2 (D) V/2 > V

(B) Even though B2 burns out, the circuit is still operating elsewhere as there are still closed paths.

B1, B2, B3, and B4 are identical light bulbs. There are six voltmeters connected to the circuit as shown. All voltmeters are connected so that they display positive voltages. Assume that the voltmeters do not affect the circuit. If B 2 were to burn out, opening the circuit, which voltmeter(s) would read zero volts? (A) none would read zero (B) only V 2 (C) only V 3 and V 4 (D) only V 2 , V 4 , and V 5

(B) 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) Both would get brighter. (B) Bulb B would get brighter and bulb C would get dimmer. (C) Bulb B would get dimmer and bulb C would get brighter. (D) Only bulb B would get brighter

(A) and (B) 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? Select two correct answers. 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) Bulb 3 is brighter than bulb 1 or 2. (B) Bulb 3 has more current passing through it than bulb 1 or 2. (C) Bulb 3 has the same voltage drop across it than bulb 1. (D) Bulb 3 has the same voltage drop across it than bulb 2.

(C) 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) 2 (B) 3 (C) 4 (D) 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

(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) Bulbs 1, 2 and 4

(D) 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) Bulb N becomes dimmer but does not go out.

(D) 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) Bulb N goes out but at least one other bulb remains lit. (C) The brightness of bulb N remains the same. (D) Bulb N becomes dimmer but does not go out.

(D) For no current to flow, the potential drop across R1 must equal the potential drop across R2. For this to occur I1R1 = I2R2. Since the two branches also have the same potential difference as a whole (they are in parallel) we also have I1(R1 + R3) = I2(R2 + R4). Solve for R3

Four resistors, R1, R2, R3, and R4, are connected in the circuit diagram above. When the switch is closed, current flows in the circuit. If no current flows through the ammeter when it is connected as shown, what would be the value of R3?

(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) 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

(D) 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) 4 Ω (C) 5 Ω (D) 6Ω

(B) 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) 10.8 V (C) 13.0 V (D) 11.6 V

(D) S1 must be closed to have any current. Closing S3 will short circuit R3, leaving only resistor R1, which is the lowest possible resistance.

In the circuit above, the resistors all have the same resistance. The battery, wires, and ammeter have negligible resistance. A closed switch also has negligible resistance Closing which of the switches will produce the greatest reading on the ammeter? (A) S 2 only (B) S 3 only (C) S 1 and S 2 (D) S 1 and S 3

(A) S1 must be closed to have any current. The greatest voltage will occur with the greatest current through R3 but closing S2 or S3 will draw current away from R3 ****use***

In the circuit above, the resistors all have the same resistance. The battery, wires, and ammeter have negligible resistance. A closed switch also has negligible resistance Closing which of the switches will produce the greatest voltage across R 3 ? (A) S 1 only (B) S 2 only (C) S 1 and S 2 only (D) S 1 and S 3 only

(D) Since there is constant current, bulb 1 remains unchanged and bulbs 2 and three must now split the current. With half the current through bulb 2, the potential difference between A and B is also halved

In the circuit shown above, a constant current device is connected to some identical light bulbs. After the switch S in the circuit is closed, which statement is correct about the circuit? (A) Bulb #2 becomes brighter. (B) Bulb #1 becomes dimmer. (C) All three bulbs become equally brighter. (D) The voltage between points C and D is decreased.

(C) 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) 15Ω (B) 20 Ω (C) 50 Ω (D) 115 Ω

(A) The total resistance of the 3 Ω and 6 Ω in parallel is 2 Ω making the total circuit resistance 6 Ωand the total current E/R = 1 A. This 1 A will divide in the ratio of 2:1 through the 3 Ω and 6 Ω respectively so the 3 Ω resistor receives 2/3 A making the potential difference IR = (2/3 A)(3Ω) = 2 V.

In the circuit shown above, what is the value of the potential difference between points X and Y if the 6-volt battery has no internal resistance? (A) 2 V (B) 3 V (C) 4 V (D) 6 V

(B) With more current drawn from the battery for the parallel connection, more power is dissipated in this connection. While the resistors in series share the voltage of the battery, the resistors in parallel have the full potential difference of the battery across them

In the diagrams above, resistors R₁ and R₂ are shown in two different connections to the same source of emf εthat has no internal resistance. How does the power dissipated by the resistors in these two cases compare? (A) It is greater for the series connection. (B) It is greater for the parallel connection. (C) It is different for each connection, but one must know the values of R₁ and R₂ to know which is greater. (D) It is different for each connection, but one must know the value of ε to know which is greater.

(B) Using ratios, the currents in the 6 Ω and 3 Ω resistors are 1 A and 2 A. They have three times and 3/2 times the resistance of the 2 Ω resistor so they will have 1/3 and 2/3 the current. The total current is then 6 A giving a potential drop of 36 V across the 6 Ω resistor in the main branch and adding any one of the branches below with the loop rule gives 36 V + 6 V = 42 V for the battery

In the electric circuit shown above, the current through the 2.0 Ω resistor is 3.0 A. Approximately what is the emf of the battery? (A) 51 V (B) 42 V (C) 36 V (D) 24 V

(B) The loop rule involves the potential and energy supplied by the battery and it's use around a circuit loop.

Kirchhoff's loop rule for circuit analysis is an expression of which of the following? (A) Conservation of charge (B) Conservation of energy (C) Ampere's law (D) Ohm's law

(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

(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

(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) R = ρL/A. Least resistance is the widest, shortest resistor (Was C in test bank)

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?

(D) The motor uses P = IV = 60 W of power but only delivers P = Fv = mgv = 45 W of power. The efficiency is "what you get" ÷ "what you are paying for" = 45/60

The operating efficiency of a 0.5 A, 120 V electric motor that lifts a 9 kg mass against gravity at an average velocity of 0.5 m/s is most nearly (A) 13% (B) 25% (C) 53% (D) 75 %

(A) 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 ½ (B) 1 (C) 2 (D) 4

(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

(A) The resistance of the two 2 Ω resistors in parallel is 1 Ω. Added to the 2 Ω resistor in series with the pair gives 3 Ω

The total equivalent resistance between points X and Y in the circuit shown above is (A) 3 Ω (B) 4 Ω (C) 5 Ω (D) 6 Ω

(C) The voltmeter is essentially another resistor. The voltmeter in parallel with the 100 Ω resistor acts as a 500 Ω resistor, which will half ½ the voltage of the 100 Ω resistor on the left. Thus the 120 V will split into 80 V for the 1000 Ω resistor and 40 V for the voltmeter combination.

Two 1000 Ω resistors are connected in series to a 120-volt electrical source. A voltmeter with a resistance of 1000 Ω is connected across the last resistor as shown. What would be the reading on the voltmeter? (A) 80 V (B) 60 V (C) 40 V (D) 30 V

(D) R = ρL/A

Two cables can be used to wire a circuit. Cable A has a lower resistivity, a larger diameter, and a different length than cable B. Which cable should be used to minimize heat loss if the same current is maintained in either cable? (A) Cable A (B) Cable B (C) The heat loss is the same for both. (D) It cannot be determined without knowing the length of each cable.

(A) P = I²R and the current is the same through each resistor.

Two resistors, one with resistance R and the second with resistance 4R are placed in a circuit with a voltage V. If resistance R dissipates power P, what would be the power dissipated by the 4R resistance? (A) 4 P (B) 2 P (C) 1/2 P (D) 1/4 P

(C) Resistance of the 2000 Ω and 6000 Ω in parallel = 1500 Ω, adding the 2500 Ω in series gives a total circuit resistance of 4000 Ω. I_total = I_1 = E/R total

What is the current I1? (A) 1.0 mA (B) 2.0 mA (C) 3.0 mA (E) 6.0 mA

(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

(D) P = V²/R

When lighted, a 100-watt light bulb operating on a 110-volt household circuit has a resistance closest to (A) 10-2 Ω (B) 10-1 Ω (C) 10 Ω (D) 100 Ω

(D) The upper branch, with twice the resistance of the lower branch, will have ½ the current of the lower branch.

When there is a steady current in the circuit, the amount of charge passing a point per unit of time is (A) the same everywhere in the circuit (B) greater in the 1 Ω resistor than in the 2 Ω resistor (C) greater at point X than at point Y (D) greater in the 2 Ω resistor than in the 3 Ω resistor

(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) One of the resistances is greater than 5 Ω, one of the resistances is less than 5 Ω.

(D) 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? (OPTION E REPLACES D])

(A) & (D) The resistances are as follows: I: 2 Ω, II: 4 Ω, III: 1 Ω, IV: 2 Ω

Which two arrangements of resistors shown above have the same resistance between the terminals? (A) I (B) II (C) III (D) IV