Physics 2: Exam 2
Suppose the resistances in the example are R1 = 2.5 Ω, R2 = 5.0 Ω and R3 = 7.5 Ω, respectively, and a new voltage source is provided. If the current measured in the 7.5-Ω resistor is 5.0 A, find the following. (a) the potential difference provided by the new battery and the currents in each of the remaining resistors (b) the power delivered to each resistor and the total power (c) the equivalent resistance (d) the total current and the power dissipated by the equivalent resistor
(a) E= I3 x R I= ∆V/R (b) Po= (Io)^2 x Ro P tot= P1 + P2 + P3 (c) Req= (1/R1) + (1/R1)...etc (d) I tot= I + I2 + I3 Peq= (∆V)^2 / Req
If electrical energy costs $0.12 per kilowatt-hour, how much do the following events cost? (a) To burn a 80.0-W lightbulb for 24 h. (b) To operate an electric oven for 4.5 h if it carries a current of 20.0 A at 220 V.
(a) E= P∆t Cost= E(rate) (b) E= (I∆V)/100 x ∆t
Batteries are rated in terms of ampere-hours (A · h). For example, a battery that can deliver a current of 3.0 A for 5.0 h is rated at 15 A · h. (a) What is the total energy, in kilowatt-hours, stored in a 9-V battery rated at 54 A · h? (b) At $0.16 per kilowatt-hour, what is the value of the electricity that can be produced by this battery?
(a) E= ∆V x I x ∆t (b) value= E x rate
A current-carrying rectangular wire loop with width a = 0.115 m and length b = 0.205 m is in the xy-plane, supported by a nonconducting, frictionless axle of negligible weight. A current of I = 2.75 A travels counterclockwise in the circuit (see the figure below). Calculate the magnitude and direction of the force exerted on the left, right, top, and bottom segments of wire (in N) by a uniform magnetic field of 0.500 T that points in the positive x-direction. Find the magnitude of the net torque (in N · m) on the loop about the axle.
(a) Fleft= BIb (b) Fright= Bib (c) Theta= 180˚ and F top=0 (d) " (e) Tnet= (a/2) (Left + Right)
A typical cellular phone consumes an average of about 1.40 W of electrical power and operates on 3.80 V. (a) What average current (in A) does the phone draw from its battery? (b) Calculate the energy (in J) stored in a fully charged battery if the phone requires charging after 8.03 hours of use.
(a) I= P/∆V (b) E= P∆t (in sec)
A heating element in a stove is designed to dissipate 3,560 W when connected to 240 V. (a) Assuming the resistance is constant, calculate the current in the heating element if it is connected to 120 V. (b) Calculate the power it dissipates at that voltage.
(a) I= P/∆V R= ∆V/I If= Vf/R (b) P= I∆V
A circuit provides a maximum current of 25.0 A at an operating voltage of 1.20 102 V. (a) How many 75 W bulbs can operate with this voltage source? (b) At $0.140 per kilowatt-hour, how much does it cost to operate these bulbs for 10.0 h? (a) How many Christmas tree lights drawing 5.00 W of power each could be run on a circuit operating at 1.20 102 V and providing 18.1 A of current? (b) Find the cost to operate one such string 24.0 h per day for the Christmas season (two weeks), using the rate $0.14/kWh.
(a) Ptotal= I∆V #bulbs= Ptotal/Pbulb (b) Energy= Pt cost= E x rate (a) P= VI #bulbs= Ptotal/Pbulb (b) E= Pt 2 weeks cost= E x rate x days
A circuit consists of a battery with a closed circuit, a terminal voltage of 12.0 V, and 1.8-Ω, 4.0-Ω, 5.5-Ω, and 7.5-Ω resistors connected in series, oriented as in figure a above, with the battery in the bottom of the loop, positive terminal on the left, and resistors in increasing order, left to right, in the top of the loop. (a) Calculate the equivalent resistance of the circuit. (b) Calculate the current. (c) Calculate the total power dissipated by the load resistors. (d) What is the electric potential at a point between the 4.0-Ω and 5.5-Ω resistors, if the electric potential at the positive terminal is 12.0 V? (e) If the battery has an emf of 12.1 V, find the battery's internal resistance. (f) What fraction f of the battery's power is delivered to the load resistors?
(a) Req= R1 + R2 + R3 + R4 (b) I= ∆V/Req (c) p= (∆V)^2 / Req (d) ∆V= IR Va-∆V (e) r= (E-∆V)/ I (f) f= ∆v/E
An uncharged capacitor and a resistor are connected in series to a battery, as shown in the figure above. If e m f = 11.0 V, C = 4.80 µF, and R = 8.70 105 Ω, find the following. (a) the time constant of the circuit (b) the maximum charge on the capacitor (c) the charge on the capacitor after 6.20 s (d) the potential difference across the resistor after 6.20 s (e) the current in the resistor at that time
(a) T= RC (b) Q= CE (c) q= Q(1-e^-t/T) (d) ∆Vc= -q/C ∆Vr= -∆Vbat-∆Vc (e) I= -∆Vr/R
(a) When two or more resistors are connected in series, the equivalent resistance is always_______ any individual resistance (b) When two or more resistors are connected in parallel, the equivalent resistance is always________ any individual resistance
(a) greater than (b) less than
The switch is closed in the figure below. After a long time compared with the time constant of the circuit, what will the current be in the 2 Ω resistor?
2A
A lightning bolt may carry a current of 1.00 104 A for a short time. What is the resulting magnetic field 60 m from the bolt? Suppose that the bolt extends far above and below the point of observation.
B= uoI/2πr
A horizontal power line of length 60 m carries a current of 2.6 kA as shown in the figure below. Earth's magnetic field at this location has a magnitude equal to 5.0 ✕ 10−5 T and makes an angle of 65° with the power line. Find the magnitude and direction of the magnetic force on the power line.
F= BIlsin(theta)
Neurons in our bodies carry weak currents that produce detectable magnetic fields. A technique called magnetoencephalography, or MEG, is used to study electrical activity in the brain using this concept. This technique is capable of detecting magnetic fields as weak as 1.0 ✕ 10−15 T. Model the neuron as a long wire carrying a current and find the current it must carry to produce a field of this magnitude at a distance of 4.7 cm from the neuron.
I= 2πrB/uo
A certain superconducting magnet in the form of a solenoid of length 0.44 m can generate a magnetic field of 5.0 T in its core when its coils carry a current of 85 A. The windings, made of a niobium-titanium alloy, must be cooled to 4.2 K. Find the number of turns in the solenoid.
N= BL/ uoI
A platinum resistance thermometer has resistances of 230.0 Ω when placed in a 0°C ice bath and 234.8 Ω when immersed in a crucible containing a melting substance. What is the melting point of this substance? (Hint: First determine the resistance of the platinum resistance thermometer at room temperature, 20.0°C.)
Ro= R/ [1+a(T-To)] T= To + (R-Ro)-(aRo)
Why is it possible for a bird to sit on a high-voltage wire without being electrocuted?
The bird is resting on a wire of fixed potential. In order to be electrocuted, a large potential difference is required between the bird's feet. The potential difference between the bird's feet is too small to harm the bird.
In the figure below the current is measured with the ammeter at the bottom of the circuit. When the switch is opened, the reading on the ammeter
decreases
In the figure below, the current is measured with the ammeter on the right side of the circuit diagram. When the switch is closed, the reading on the ammeter
increases
Consider the mass spectrometer shown schematically in the figure below. The electric field between the plates of the velocity selector is 900 V/m, and the magnetic fields in both the velocity selector and the deflection chamber have magnitudes of 0.950 T. Calculate the radius r of the path for a singly charged ion with mass m = 2.02 ✕ 10−26 kg.
r= mE/ qB^2
What magnetic force is exerted on a wire carrying current parallel to the direction of the magnetic field?
zero
A proton moves at 7.97 106 m/s along the x-axis. It enters a region in which there is a magnetic field of magnitude 2.59 T, directed at an angle of 60.0° with the x-axis and lying in the xy-plane (see figure). (a) Find the initial magnitude and direction of the magnetic force on the proton. (b) Calculate the proton's initial acceleration. Calculate the acceleration of an electron that moves through the same magnetic field as in the example, as the same velocity as the proton. The mass of an electron is 9.11 10-31 kg.
(a) F= qvsin(theta) (b) a= F/m (a) a= F/m
A wire carries a current of 22.6 A from west to east. Assume that at this location the magnetic field of Earth is horizontal and directed from south to north and that it has a magnitude of 5.00 10-5 T. (a) Find the magnitude and direction of the magnetic force on a 38.3 m length of wire. (b) Calculate the gravitational force on the same length of wire if it's made of copper and has a cross-sectional area of 2.30 10-6 m2. What current would make the magnetic force in the example equal in magnitude to the gravitational force?
(a) F=BIL sin(theta) (b) m= p(Al) Fgrav=mg (a) I= Fg/Bl
A coffee maker is rated at 1180 W, a toaster at 1120 W, and a waffle maker at 1380 W. The three appliances are connected in parallel to a common 120 V household circuit. (a) What is the current in each appliance when operating independently? (b) What total current is delivered to the appliances when all are operating simultaneously? (c) Is a 15-A circuit breaker sufficient in this situation? Explain
(a) I= P/∆V (b) I tot= I + I2 + I3 (c) No. The total current required exceeds the limit of the circuit breaker, so they cannot be operated simultaneously. In fact, with a 15 A limit, no two of these appliances could be operated at the same time without tripping the breaker.
A proton moves with a speed of 1.39 105 m/s through Earth's magnetic field, which has a value of 52.7 µT at a particular location. When the proton moves eastward, the magnetic force acting on it is directed straight upward, and when it moves northward, no magnetic force acts on it. (a) What is the direction of the magnetic field? (b) What is the strength of the magnetic force when the proton moves eastward? (c) Calculate the gravitational force on the proton and compare it with the magnetic force. Compare it also with the electric force if there were an electric field with magnitude E = 1.50 102 N/C at that location, a common value at Earth's surface. Note that the mass of the proton is 1.67 10-27 kg. Suppose an electron is moving due west in the same magnetic field as in the example at a speed of 2.67 105 m/s. Find the magnitude and direction of the magnetic force on the electron.
(a) North (b) F= qvBsin (theta) (c) Fgrav=mg Felec= qE (a) F= qvBsin90
The orientation of small satellites is often controlled using torque from current-carrying coils in Earth's magnetic field. Suppose a multiturn coil has a cross-sectional area of 6.46 ✕ 10−4 m2, dissipates 0.250 W of electrical power from a 5.50 V power supply, and provides a magnetic moment of magnitude 0.0400 A · m2. (a) Find the coil current I (in A). (b) Calculate the number of turns in the coil. (c) Calculate the maximum magnitude of torque (in N · m) if Earth's magnetic field has magnitude 3.70 ✕ 10−5 T at the satellite's location.
(a) P= I/V (b) N= u/ IA (c) Tmax= uB
An uncharged capacitor and a resistor are connected in series to a source of emf. If e m f = 11.00 V, C = 18.0 µF, and R = 100 Ω, find the following: (a) the time constant of the circuit (b) the maximum charge on the capacitor (c) the charge on the capacitor after one time constant
(a) T= RC (b) Qmax= CE (c) Q= Qmax (1- 1/e)
A certain solenoid consists of 141 turns of wire and has a length of 13.2 cm. (a) Find the magnitude of the magnetic field inside the solenoid when it carries a current of 0.650 A. (b) What is the momentum of a proton orbiting inside the solenoid in a circle with a radius of 0.023 m? The axis of the solenoid is perpendicular to the plane of the orbit. (c) Approximately how much wire would be needed to build this solenoid? Assume the solenoid's radius is 5.18 cm. Suppose you have a 32.7 m length of copper wire. If the wire is wrapped into a solenoid 0.240 m long and having a radius of 0.0511 m, how strong is the resulting magnetic field in its center when the current is 12.4 A?
(a) n= N/l B= uonI (b) p=mv= rqB (c) Length= turns x 2πr (a) B= [(l/2πr) / wire] I x uo
Consider a capacitor C being discharged through a resistor R as shown in figure a. The initial potential difference across the capacitor is 18.0 V, the capacitance is 2.30 10-6 F, and the resistance is 1.90 Ω. (a) How long does it take for the charge on the capacitor to drop to one-fourth of its initial value? (b) Compute the initial charge and time constant. (c) How long does it take to discharge all but the last quantum of charge, 1.6 10-19 C? (Assume an exponential decrease during the entire discharge process.) (a) How long does it take the capacitor to lose half its initial charge? (b) How long does it take to lose all but the last 10 electrons on the negative plate?
(a) t= -RC ln(1/4) (b) Q= C∆V T= RC (c) t= -T ln (q/Q) (a) t= -RC ln (1/2) (b) t= RC x ln (C∆V/10e)
A circular wire loop of radius 1.28 m is placed in a magnetic field of magnitude 0.510 T. The normal to the plane of the loop makes an angle of 30.0° with the magnetic field (see figure a). The current in the loop is 2.30 A in the direction shown. (a) Find the magnetic moment of the loop and the magnitude of the torque at this instant. (b) The same current is carried by the rectangular 2.00 m by 3.00 m coil with three loops shown in figure b. Find the magnetic moment of the coil and the magnitude of the torque acting on the coil at that instant. Suppose a right triangular coil with base of 2.05 m and height 2.95 m having two loops carries a current of 2.30 A as shown in figure c. Find the magnetic moment and the torque on the coil. The magnetic field is 0.510 T and makes an angle of 30.0° with respect to the normal direction.
(a) u= Iπr^2N (b) A= L x H u= IAN T= uBsin(theta) (a) u= IAN T= uBsin(theta)
Using an electromagnetic flowmeter (see the figure below), a heart surgeon monitors the flow rate of blood through an artery. Electrodes A and B make contact with the outer surface of the blood vessel, which has interior diameter 2.70 mm. (a) For a magnetic field magnitude of 0.0390 T, a potential difference of 160 μV appears between the electrodes. Calculate the speed of the blood. (b) Verify that electrode A is positive, as shown. Does the sign of the emf depend on whether the mobile ions in the blood are predominantly positively or negatively charged? Explain.
(a) v= ∆V/Bd (b) The magnetic field is directed from N to S. If the charge carriers are negative moving in the direction of v, the magnetic force is directed toward point B. Negative charges build up at point B, making the potential at A higher than at B. If the charge carriers are positive moving in the direction of v, the magnetic force is directed toward A, so positive charges build up at A. This also makes the potential at Indicate the direction with the sign of your answer. higher than at B. Therefore, the sign of the potential difference does not depend on the charge of the ions.
Two charged particles are projected into a region where a magnetic field is directed perpendicular to their velocities. If the charges are deflected in opposite directions, what are the possible relative charges and directions?
-same charge, opposite initial direction -oppositely charged, same initial direction
A cardiac pacemaker can be affected by a static magnetic field as small as 1.7 mT. How close can a pacemaker wearer come to a long, straight wire carrying 27 A?
r= uoI/ 2πB
A square and a circular loop with the same area lie in the xy-plane, where there is a uniform magnetic field vector B pointing at some angle θ with respect to the positive z-direction. Each loop carries the same current, in the same direction. Which magnetic torque is larger?
the torques are the same