April 8, 1999


Charge in a capacitor: q = CV

Flat plate capacitor: C = e0A/d

Cylindrical capacitor: C = 2 p e0 L / ln (b/a)

Electric potential energy: U = q2/2C = ½ C V2

Definition of resistance: R = V/i

Definition of resistivity: r = E/J = (V/m)/(A/m2)

Power dissipated: P = iR2 = V2/R = Vi

Magnetic force : F = q v x B

Circular motion in a magnetic field: r = mv/qB

Magnetic force on a wire: F = iL x B


Complete all of the following multiple choice (4 points each)

[1] Three capacitors, each rated at 2 mF , are attached in series. What is the equivalent capacitance?

A) 0.50 mF B) 0.66 mF C) 1.5 mF D) 2.0 mF E) 6.0 mF

[2] A crazy physics professor decides to blow up a ceramic capacitor in class by applying too much voltage. The capacitor is rated at 1 mF and 100 V. The capacitor exploded at 400 V. How much energy was released in the explosion?

A) 0.0004 J B) 0.0025 J C) 0.08 J D) 0.16 J E) 0.4 J

[3] Which circuit has the largest equivalent capacitance?

A) B) C) D) E) all of the above (explain)

[4] The following table gives the current i,(in amperes) through two devices for several values of potential difference V (in volts). From these data, determine which device(s) obey Ohm’s law.

Device 1 Device 2 Device 3

V i V i V i

2.00 4.50 2.00 1.50 2.00 2.33

3.00 6.75 3.00 2.20 3.00 2.00

4.00 9.00 4.00 2.80 4.00 1.66

A) a B) b C) c D) a & c E) none of the above

[5] The following figure shows cross sections through three wires of equal length and of the same material. The figure also gives the length of each side in millimeters. Rank the wires according to their resistances (measured end to end along each wire’s length), greatest first.


DrawObject 4 (a) 3 (c)

2 (b)

4 5 6

A) a b c B) b a c C) c a b D) a c b E) c b a F) b c a

[6] If in the figure above, (a) is made from Cu, (b) from Ag, and (c) from Al, what would be the ranking of resistances? (Resistivity, r in nW-m is the following: Cu=16.9, Ag=16.2, Al=27.5)

A) a b c B) b a c C) c a b D) a c b E) c b a F) b c a

[7] A battery has an emf of 12 V and an internal resistance of 2 W. Is the terminal-to-terminal potential difference greater than (>), less than (<), or equal to (=) 12V if the current in the battery is (a) from the negative to the positive terminal, (b) from the positive terminal to the negative terminal, and (c) zero?

A) >,<,= B)<,>,= C)<,=,> D)>,=,< E) =,<,>

[8] In the following figure, all the resistors have a resistance of 4.0 W, and all the batteries are ideal with an emf of 4.0 V. What is the current through resistor R?

A) 0.25 A B) 0.5 A C) 1.0 A D) 2.0 A E) 4.0 A

[9] Determine the potential difference across capacitor C2 in the following figure.

A) 15 V B)20 V C) 30 V D) 35 V E) 45 V

[10]The following figure shows four directions for the velocity vector v of a positively charged particle moving through a uniform electric field E (directed out of the page and represented by an encircled dot) and a uniform magnetic field B. Rank the directions 1, 2, and 3 according to the magnitude of the net force on the particle, greatest first.

A) 1,2,3 B) 2, 1, 3 C) 1, 3, 2 D) 3, 2, 1 E) 3, 1, 2

[11] In the following picture, a proton and an electron are travelling at the same speed in a uniform magnetic field B which points into the page. Which figure(s) are labelled correctly?

DrawObjectDrawObjectDrawObjectDrawObjectDrawObjectDrawObjectDrawObjectDrawObjectDrawObjectDrawObjectDrawObject p+ p+ e- e-

DrawObject e- e- p+ p+


(a) (b) (c) (d)

A) a B) b C) c D) d E) none of the above (explain)

[12] The dead-quiet “caterpillar drive” for submarines in the movie The Hunt for Red October is based on a magnetohydrodynamic drive: as the ship moves forward, seawater flows through multiple channels in a structure built around the rear of the hull. The follwing figure shows the esse4ntials of a channel. Magnets, positioned along opposite sides of the channel with opposite poles facing each other, create a magnetic field within the channel. Electrodes (not shown) create an electric field across the channel. The electric field drives a current across the channel and through the water; the magnetic force on the current propels the water twoward the rear of the channel, thus propelling the ship forward. In the figure, should the electric field be directed up, down, left, right, front or back?

A) up B) down C) left D) right E) front F) back

Choose any 3 of the following 4 problems (12 points each):

[13] You are asked to construct a capacitor having a capacitance near 1 nF and a breakdown potential in excess of 10,000 V. You think of using the sides of a tall Pyrex drinking glass as a dielectric, lining the inside and outside curved surfaces with aluminum foil. The glass is 15 cm tall with an inner radius of 3.8 cm and an outer radius of 4.0 cm. What are the (a) capacitance and (b) breakdown potential? (Pyrex has dielectric constant k=4.7, dielectric strength of 14kV/mm.)

[14] A 1000 W radiant heater is constructed to operate at 115 V. (a) What will be the current in the heater? (b) What is the resistance of the heating coil? (c) how much thermal energy is generated in 1.0 hour by the heater?

[15] (a) In the following circuit, what value must R have if the current in the circuit is to be 1.0 mA? Take E1= 6.0 V, E2 = 9.0 V, and r1 = r2 = 3.0 W. (b) What is the rate at which thermal energy appears in R?


DrawObjectDrawObjectDrawObjectDrawObject E1 E2

r1 r2


[16] An electron is accelerated from rest by a potential difference of 400 V. It then enters a uniform magnetic field of magnitude 200 mT with its velocity perpendicular to the field. Calculate (a) the speed of the electron and (b) the radius of its path in the magnetic field.