Q: A parallel plate capacitor is designed to have a capacitance of 1 F. If the plate separation is $$d = 1 mm $$and the dielectric is air ($$\kappa = 1$$), what is the required plate area $$A$$?

$$A = 1.13 \times 10^7$ \text{ m}^2$$

Question 1

A parallel plate capacitor has plates of area $$A$$ and separation $$d. If $$the plates carry charges $$+q$$ and $$-q$$, what is the magnitude of the electric field between the plates (ignoring edge effects)?

Accepted Answer

$$E = \frac{q}{\$$epsilon_0$$ A}$$

Question 2

The potential difference $$V$$ across a parallel plate capacitor is related to the electric field $$E$$ and plate separation $$d by $$which equation?

Accepted Answer

$$V = Ed$$

Question 3

A capacitor is filled with a dielectric material of dielectric constant $$\kappa. $$How does the capacitance change compared to the same capacitor with air between the plates?

Accepted Answer

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

Question 4

If a parallel plate capacitor is connected to a battery and a dielectric is inserted between the plates, what happens to the charge stored on the plates?

Accepted Answer

The charge increases

Question 5

If a parallel plate capacitor is charged and then disconnected from the battery, and a dielectric is inserted, what happens to the voltage across the plates?

Accepted Answer

The voltage decreases

Question 6

Which equation gives the capacitance $$C of a $$parallel plate capacitor with plate area $$A$$, separation $$d$$, and dielectric constant $$\kappa$$?

Accepted Answer

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

Question 7

A computer keyboard uses capacitors to detect key presses. When a key is pressed, the plate separation decreases. What happens to the capacitance?

Accepted Answer

The capacitance increases

Question 8

Which of the following substances has the highest dielectric constant according to the provided table?

Accepted Answer

Water

Question 9

The energy stored in a capacitor is given by which equation?

Accepted Answer

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

Question 10

A parallel plate capacitor with plate area $$A$$ and separation $$d is $$filled with a dielectric of strength $$S. $$What is the maximum voltage $$V_{max}$$ that can be applied before breakdown?

Accepted Answer

$$V_{max} = S \cdot d$$

Question 11

If the energy density in the electric field of a capacitor is $$u = \frac{1}{2}\kappa\$$epsilon_0$$ E^2$, what happens to the energy density when a dielectric is inserted and the electric field remains constant?

Accepted Answer

The energy density increases by a factor of $$\kappa$$

Question 12

A parallel plate capacitor is designed to have a capacitance of 1 F. If the plate separation is $$d = 1 mm $$and the dielectric is air ($$\kappa = 1$$), what is the required plate area $$A$$?

Accepted Answer

$$A = 1.13 	imes 10^7$ 	ext{ m}^2$$

Question 13

Which of the following statements about equipotential surfaces in a parallel plate capacitor is correct?

Accepted Answer

Equipotential surfaces are perpendicular to the electric field lines

Question 14

A 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

The energy decreases

Question 15

A capacitor is charged to a voltage $$V$$ and remains connected to the battery. If a dielectric is inserted, what happens to the energy stored in the capacitor?

Accepted Answer

The energy increases

Question 16

Which of the following is NOT an advantage of using a dielectric in a capacitor?

Accepted Answer

It decreases the ability to store charge

Question 17

The charge density $$\sigma on a $$parallel plate capacitor is given by which equation?

Accepted Answer

$$\sigma = \frac{q}{A}$$

Question 18

A point charge $$q$$ creates an electric field $$E at a $$distance $$r in $$air. What is the energy density of the electric field at that point?

Accepted Answer

$$u = \frac{1}{2}\$$epsilon_0$$ E^2$

Question 19

Which scenario best describes the effect of inserting a dielectric slab into a capacitor with constant charge?

Accepted Answer

The voltage across the plates decreases

Lec 5

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