Question 1

A parallel-plate capacitor is connected to a 12 V battery and has plates of area $$A$$ separated by a distance $$d. $$What is the correct expression for its capacitance in vacuum?

Accepted Answer

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

Question 2

If the area of the plates of a parallel-plate capacitor is doubled while the separation is halved, how does the capacitance change?

Accepted Answer

It is quadrupled.

Question 3

A capacitor is charged and then disconnected from the battery. If the separation between the plates is increased, what happens to the voltage across the plates?

Accepted Answer

The voltage increases.

Question 4

Which of the following best describes the effect of inserting a dielectric with dielectric constant $$\kappa$$ between the plates of a capacitor connected to a battery?

Accepted Answer

The capacitance increases by a factor $$\kappa.$$

Question 5

Three capacitors, $$C_1$$, $$C_2$$, and $$C_3$$, are connected in series. Which equation correctly gives the equivalent capacitance $$C_{eq}$$?

Accepted Answer

$$\dfrac{1}{C_{eq}} = \dfrac{1}{C_1$} + \dfrac{1}{C_2$} + \dfrac{1}{C_3$}$$

Question 6

A camera flash uses a capacitor to store energy. If the capacitor has a capacitance $$C$$ and is charged to a voltage $$V$$, what is the energy stored?

Accepted Answer

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

Question 7

The energy density $$u in $$the electric field between the plates of a parallel-plate capacitor is given by which expression?

Accepted Answer

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

Question 8

A cylindrical capacitor consists of two coaxial cylinders of length $$\ell$$, inner radius $$R_a$$, and outer radius $$R_b. $$What is the correct formula for its capacitance?

Accepted Answer

$$C = 2\pi \$$varepsilon_0$$ \dfrac{\ell}{\ln(R_b/R_a)}$$

Question 9

In a DRAM memory cell, the capacitor must retain charge for a short period. Which property of the dielectric is most important for minimizing charge leakage?

Accepted Answer

High dielectric strength

Question 10

A parallel-plate capacitor is filled with a dielectric material of dielectric constant $$\kappa. If $$the original capacitance was $$C_0$$, what is the new capacitance?

Accepted Answer

$$C = \kappa C_0$

Question 11

Which of the following best explains why 'low-k' dielectrics are used in modern integrated circuits?

Accepted Answer

They decrease the capacitance between interconnects, reducing signal delay.

Question 12

A capacitor is connected to a battery and a dielectric is inserted between the plates. Which of the following statements is true?

Accepted Answer

The charge on the plates increases.

Question 13

Which material from the table has the highest dielectric constant and is therefore most suitable for use in high-capacitance capacitors?

Accepted Answer

Strontium titanate

Question 14

A MOS transistor uses a gate dielectric with dielectric constant $$\kappa_{ox}$$ and thickness $$t_{ox}. $$What is the correct expression for the gate capacitance per unit area $$C_{ox}$$?

Accepted Answer

$$C_{ox} = \dfrac{\kappa_{ox} \$$varepsilon_0$$}{t_{ox}}$$

Question 15

Which of the following is a correct statement about the energy stored in a capacitor?

Accepted Answer

It is proportional to the square of the charge stored.

Question 16

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

Accepted Answer

It decreases by a factor $$\kappa.$$

Question 17

Which of the following best describes the molecular mechanism by which a dielectric increases the capacitance of a capacitor?

Accepted Answer

It aligns its polar molecules to reduce the effective electric field.

Question 18

In a parallel connection of capacitors, which of the following is true?

Accepted Answer

The equivalent capacitance is the sum of the individual capacitances.

Question 19

A capacitor is used in a touch screen sensor. Which property of the capacitor is most directly utilized in detecting a finger touch?

Accepted Answer

The change in capacitance due to the presence of a finger.

Capacitors and Dielectrics: Principles, Calculations, and Applications

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