Question 1

A spherical capacitor consists of two concentric spherical conductors with radii $$a$$ and $$b$$ ($$a \u003c b). If $$the inner sphere carries charge $$+q$$ and the outer sphere carries charge $$-q$$, what is the expression for the capacitance $$C of $$this spherical capacitor?

Accepted Answer

$$C = \frac{4\pi\$$epsilon_0$$ ab}{b-a}$$

Question 2

In the diagram of a spherical capacitor, what is the purpose of the Gaussian surface shown between the two spheres?

Accepted Answer

To calculate the electric field at a distance $$r$$ from the center using Gauss's law

Question 3

A cylindrical capacitor consists of two coaxial cylinders of radii $$a$$ and $$b$$ ($$a \u003c b) $$and length $$L. $$What is the formula for its capacitance?

Accepted Answer

$$C = \frac{2\pi\$$epsilon_0$$ L}{\ln(b/a)}$$

Question 4

Which of the following best describes the difference between potential difference and potential drop?

Accepted Answer

Potential difference is final minus initial; potential drop is initial minus final

Question 5

A parallel-plate capacitor has plates of area $$A$$ separated by distance $$d. $$What is the capacitance $$C$$?

Accepted Answer

$$C = \frac{\$$epsilon_0$$ A}{d}$$

Question 6

If the temperature of a metallic conductor increases, what happens to its resistance?

Accepted Answer

Resistance increases

Question 7

A current $$I$$ flows through a wire of cross-sectional area $$A. $$What is the current density $$J$$?

Accepted Answer

$$J = \frac{I}{A}$$

Question 8

A cylindrical wire of radius $$r_1$$ carries a current density $$J_1. If $$another wire of radius $$r_2$$ carries the same total current, what is the current density $$J_2 in $$the second wire?

Accepted Answer

$$J_2$$ = \frac{$$r_1^2$$ $$J_1$$}{$$r_2^2$$}$$

Question 9

Which of the following statements about capacitors is correct?

Accepted Answer

Capacitors store energy in the electric field between their plates

Question 10

A capacitor is charged to a voltage $$V$$ and then disconnected from the battery. If the plates are moved farther apart, what happens to the stored energy?

Accepted Answer

The stored energy increases

Question 11

A student measures the current through a resistor and finds it to be $$0.5 A $$when a voltage of $$10 V is $$applied. What is the resistance?

Accepted Answer

$$R = 20\ \Omega$$

Question 12

Which of the following is a plausible real-world application of a cylindrical capacitor?

Accepted Answer

Used in coaxial cables for signal transmission

Question 13

If a capacitor is connected to a battery and the dielectric constant of the material between the plates is increased, what happens to the capacitance?

Accepted Answer

Capacitance increases

Question 14

A spherical capacitor has inner radius $$a = 1 cm $$and outer radius $$b = 2 cm. $$What is the capacitance in terms of $$\$$epsilon_0$$?

Accepted Answer

$$C = \frac{4\pi\$$epsilon_0$$ \cdot 1 \cdot 2}{2-1}$$

Question 15

A parallel-plate capacitor is used in a defibrillator. If the plates are $$0.01 m $$apart and have an area of $$0.05 m$^2$$, what is the capacitance (in terms of $$\$$epsilon_0$$)?

Accepted Answer

$$C = \frac{\$$epsilon_0$$ \cdot 0.05}{0.01}$$

Question 16

A wire of radius $$r_1$$ carries a current density $$J_1. If a $$second wire of radius $$r_3$$ carries the same total current, what is the current density $$J_3$$?

Accepted Answer

$$J_3$$ = \frac{$$r_1^2$$ $$J_1$$}{$$r_3^2$$}$$

Question 17

Which of the following best describes the relationship between current and emf in a circuit?

Accepted Answer

Current is directly proportional to emf and inversely proportional to resistance

Question 18

A capacitor is used in a pacemaker to deliver a controlled pulse. If the voltage across the capacitor is $$V$$ and the capacitance is $$C$$, what is the stored energy?

Accepted Answer

$$U = \frac{1}{2}CV^2$

Capacitors and Electric Current: Key Concepts and Applications

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