Q: A $$10\,\mu\mathrm{F}$$ and a $$20\,\mu\mathrm{F}$$ capacitor are connected in series across a $$100\,\mathrm{V}$$ battery. What is the equivalent capacitance?

$$C_{eq} = \dfrac{10 \times 20}{10 + 20} = 6.67\,\mu\mathrm{F}$$

Question 1

A parallel-plate capacitor has plates of area $$A$$ separated by a distance $$d in $$vacuum. Which of the following correctly expresses its capacitance?

Accepted Answer

$$C = \$$varepsilon_0$$ \dfrac{A}{d}$$

Question 2

If the separation $$d$$ between the plates of a parallel-plate capacitor is halved while keeping the area $$A$$ and charge $$Q$$ constant, what happens to the electric field $$E$$ between the plates?

Accepted Answer

$$E$$ remains the same

Question 3

A spherical capacitor consists of two concentric spherical shells of radii $$r_a$$ and $$r_b$$ ($$r_b \u003e r_a). $$What is the expression for its capacitance?

Accepted Answer

$$C = 4\pi \$$varepsilon_0$$ \dfrac{r_a r_b}{r_b - r_a}$$

Question 4

Two capacitors, $$C_1$$ and $$C_2$$, are connected in series across a battery of voltage $$V. $$What is the charge on each capacitor?

Accepted Answer

Both capacitors have the same charge $$Q$$

Question 5

Which of the following is true for capacitors connected in parallel?

Accepted Answer

The total capacitance is the sum of individual capacitances: $$C_{eq} = C_1$ + C_2$ + \ldots$$

Question 6

A parallel-plate capacitor is connected to a battery and then the plate separation is decreased. Which of the following quantities increase?

Accepted Answer

Capacitance, charge, energy stored, energy density

Question 7

The energy stored in a capacitor is given by which of the following expressions?

Accepted Answer

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

Question 8

A dielectric material with dielectric constant $$K is $$inserted between the plates of a parallel-plate capacitor while it is disconnected from the battery. What happens to the voltage across the plates?

Accepted Answer

The voltage decreases by a factor of $$K$$

Question 9

Which of the following best describes the effect of inserting a dielectric between the plates of a capacitor connected to a battery?

Accepted Answer

Capacitance increases, more charge flows onto the plates, voltage remains constant

Question 10

A cylindrical capacitor consists of two coaxial cylinders of length $$L$$, radii $$a$$ and $$b$$ ($$b \u003e a). $$What is the expression for its capacitance?

Accepted Answer

$$C = \dfrac{2\pi \$$varepsilon_0$$ L}{\ln(b/a)}$$

Question 11

The energy density $$u of $$the electric field in a vacuum is given by:

Accepted Answer

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

Question 12

A $$10\,\mu\mathrm{F}$$ and a $$20\,\mu\mathrm{F}$$ capacitor are connected in series across a $$100\,\mathrm{V}$$ battery. What is the equivalent capacitance?

Accepted Answer

$$C_{eq} = \dfrac{10 	imes 20}{10 + 20} = 6.67\,\mu\mathrm{F}$$

Question 13

A parallel-plate capacitor is charged and then disconnected from the battery. If the plate separation is doubled, what happens to the energy stored in the capacitor?

Accepted Answer

Question 14

Which of the following statements about the breakdown potential of a dielectric is correct?

Accepted Answer

It is the maximum potential difference before the dielectric becomes conductive and sparks

Question 15

A capacitor is charged to a voltage $$V$$ and then disconnected from the battery. If a dielectric with constant $$K is $$inserted, what happens to the energy stored in the capacitor?

Accepted Answer

The energy decreases by a factor of $$K$$

Question 16

Which of the following is a practical application of capacitors in real life?

Accepted Answer

Storing and releasing energy quickly in devices like the Z machine for nuclear fusion experiments

Question 17

A parallel-plate capacitor with area $$A$$ and separation $$d is $$filled with a dielectric of constant $$K. $$What is the new capacitance?

Accepted Answer

$$C = K \$$varepsilon_0$$ \dfrac{A}{d}$$

Question 18

Which of the following best describes the effect of a dielectric on the electric field between the plates of a capacitor?

Accepted Answer

The electric field decreases due to polarization of the dielectric

Capacitance and Capacitors: Principles, Types, and Applications

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