Q: A 220 $$\muF $$camera-flash capacitor is charged to 330 V and then discharged in 1.0 ms. What is the average power dissipated during the discharge?

$$P = \dfrac{1}{2} C V^2$ / t = \dfrac{1}{2} \times 220 \times 10$$^{-6}$$ \times (330)^2$ / (1.0 \times 10$$^{-3}$$) = 12,000 W$$

Question 1

A parallel-plate capacitor with plate area $$A$$ and separation $$d is $$connected to a battery of emf $$\mathcal{E}. If a $$dielectric with dielectric constant $$\kappa is $$inserted fully between the plates while the battery remains connected, which of the following statements is correct?

Accepted Answer

The capacitance increases by a factor of $$\kappa$$, and the charge on the plates increases.

Question 2

Which of the following best describes the relationship between the electric field $$\vec{E}$$ and the electric potential $$V in a $$region of space?

Accepted Answer

$$\vec{E} is $$always perpendicular to equipotential surfaces and points in the direction of decreasing $$V.$$

Question 3

A 220 $$\muF $$camera-flash capacitor is charged to 330 V and then discharged in 1.0 ms. What is the average power dissipated during the discharge?

Accepted Answer

$$P = \dfrac{1}{2} C V^2$ / t = \dfrac{1}{2} 	imes 220 	imes 10$$^{-6}$$ 	imes (330)^2$ / (1.0 	imes 10$$^{-3}$$) = 12,000 W$$

Question 4

A 5.0 nF parallel-plate capacitor is charged to 160 V and then disconnected from the battery. It is then immersed in distilled water ($$\kappa = 80). $$What happens to the voltage across the capacitor?

Accepted Answer

The voltage decreases by a factor of 80.

Question 5

Which of the following is true for a conductor in electrostatic equilibrium?

Accepted Answer

Any excess charge resides on the surface, and the entire conductor is at the same potential.

Question 6

A battery does $$4.8 	imes 10$$^{-19}$$ J of work to move each positive ion from the negative to the positive terminal. What is the emf of the battery?

Accepted Answer

Question 7

A capacitor is charged to a potential difference $$V$$ and stores energy $$U. If $$the potential difference is doubled, what happens to the stored energy?

Accepted Answer

It increases by a factor of four.

Question 8

Which of the following statements about capacitors in series is correct?

Accepted Answer

The equivalent capacitance is less than any individual capacitance in the series.

Question 9

The energy density $$u of $$the electric field inside a parallel-plate capacitor is given by which of the following expressions?

Accepted Answer

$$u = \dfrac{1}{2} \$$varepsilon_0$$ E^2$

Question 10

A metal sphere is placed near a flat metal plate and both are connected to a battery. Which statement best describes the equipotential surfaces near the electrodes?

Accepted Answer

The equipotential surfaces near each electrode roughly match the shape of the electrode.

Question 11

A 3.0 $$\muF $$and a 6.0 $$\muF $$capacitor are connected in parallel across a battery. What is their equivalent capacitance?

Accepted Answer

$$9.0\ \muF$$

Question 12

Which of the following is a property of a dielectric material inserted between the plates of a capacitor?

Accepted Answer

It increases the maximum electric field the capacitor can sustain before breakdown.

Question 13

A point charge $$q$$ creates an electric potential $$V(r) = \dfrac{1}{4\pi\$$varepsilon_0$$} \dfrac{q}{r}. $$What is the magnitude of the electric field at distance $$r$$ from the charge?

Accepted Answer

$$E = \dfrac{1}{4\pi\$$varepsilon_0$$} \dfrac{q}{r^2$}$$

Question 14

A defibrillator contains a 150 $$\muF $$capacitor charged to 2100 V. What is the energy stored in the capacitor?

Accepted Answer

$$U = \dfrac{1}{2} C V^2$ = \dfrac{1}{2} 	imes 150 	imes 10$$^{-6}$$ 	imes (2100)^2$ = 330 J$$

Question 15

Which of the following statements about the electric field inside a conductor in electrostatic equilibrium is correct?

Accepted Answer

The electric field is zero everywhere inside the conductor.

Question 16

A 2.0 $$\muF $$and a 6.0 $$\muF $$capacitor are connected in series. What is their equivalent capacitance?

Accepted Answer

$$1.5\ \muF$$

Question 17

An electron is released from rest at a point where the electric potential decreases with increasing $$x. $$What does the electron do immediately after being released?

Accepted Answer

It moves to the left with increasing speed.

Question 18

Kirchhoff’s loop law states that:

Accepted Answer

The sum of all potential differences around a closed path is zero.

Question 19

The SI unit of capacitance is:

Accepted Answer

farad

Question 20

Which of the following best describes the effect of inserting a dielectric with dielectric constant $$\kappa$$ into a capacitor while keeping the charge constant?

Accepted Answer

The capacitance increases by a factor of $$\kappa$$, and the voltage decreases by a factor of $$\kappa.$$

Chapter 26: Potential and Field – Study Notes

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