Q: A defibrillator, as shown in the first image, uses a capacitor to deliver a rapid pulse of energy to a patient's heart. If a defibrillator stores 200 J of energy at a voltage of 5000 V, what is the capacitance of the capacitor used?

$$C = \frac{2U}{(\Delta V)^2$} = \frac{2 \times 200}{(5000)^2$} = 0.016 \text{ mF}$$

Q: A 72 pF capacitor is connected to a 10 V battery. How much charge is stored on the capacitor?

$$Q = C \Delta V = 72 \times 10$$^{-12}$$ \times 10 = 720 \times 10$$^{-12}$$ \text{ C}$$

Q: The earth-ionosphere system can be modeled as a capacitor. If the earth carries $$5 \times 10^5$ C of charge and the potential difference is 3$$ \times $$10^5 V$$, what is the capacitance?

$$C = \frac{Q}{\Delta V} = \frac{5 \times 10^5$}{3 \times 10^5$} = 1.67 \text{ F}$$

Q: If the bottom of the ionosphere is 60 km above the surface and the potential difference between the earth and ionosphere is $$3 \times 10^5$ V, what is the magnitude of the average electric field?

$$E = \frac{\Delta V}{d} = \frac{3 \times 10^5$}{60 \times 10^3$} = 5 \text{ V/m}$$

Question 1

A defibrillator, as shown in the first image, uses a capacitor to deliver a rapid pulse of energy to a patient's heart. If a defibrillator stores 200 J of energy at a voltage of 5000 V, what is the capacitance of the capacitor used?

Accepted Answer

$$C = \frac{2U}{(\Delta V)^2$} = \frac{2 	imes 200}{(5000)^2$} = 0.016 	ext{ mF}$$

Question 2

Which of the following best describes the primary function of a capacitor in an electronic flash circuit, as seen in the second image?

Accepted Answer

To store electrical energy and release it rapidly to produce a bright flash

Question 3

A parallel plate capacitor is connected to a battery, as shown in the third image. If the plates are pulled apart while the battery remains connected, what happens to the charge on the plates?

Accepted Answer

The charge decreases because the capacitance decreases and the battery maintains the voltage

Question 4

The energy stored in a capacitor is given by $$U = \frac{1}{2} Q \Delta V. If a $$capacitor is charged to a voltage $$\Delta V$$ and then disconnected from the battery, what happens to the energy stored if a dielectric is inserted between the plates?

Accepted Answer

The energy decreases because the capacitance increases and the charge remains constant

Question 5

A 72 pF capacitor is connected to a 10 V battery. How much charge is stored on the capacitor?

Accepted Answer

$$Q = C \Delta V = 72 	imes 10$$^{-12}$$ 	imes 10 = 720 	imes 10$$^{-12}$$ 	ext{ C}$$

Question 6

If the potential difference across a capacitor is doubled, what happens to its capacitance?

Accepted Answer

It remains unchanged

Question 7

A charged, isolated capacitor has a charge $$Q. $$The plates are then pulled apart so that the distance between them is larger. What happens to the electric field between the plates?

Accepted Answer

The electric field remains constant because the charge is constant

Question 8

The earth-ionosphere system can be modeled as a capacitor. If the earth carries $$5 	imes 10^5$ C of charge and the potential difference is 3$$ 	imes $$10^5 V$$, what is the capacitance?

Accepted Answer

$$C = \frac{Q}{\Delta V} = \frac{5 	imes 10^5$}{3 	imes 10^5$} = 1.67 	ext{ F}$$

Question 9

If the bottom of the ionosphere is 60 km above the surface and the potential difference between the earth and ionosphere is $$3 	imes 10^5$ V, what is the magnitude of the average electric field?

Accepted Answer

$$E = \frac{\Delta V}{d} = \frac{3 	imes 10^5$}{60 	imes 10^3$} = 5 	ext{ V/m}$$

Question 10

Which material would result in the greatest increase in capacitance when used as a dielectric in a capacitor?

Accepted Answer

Strontium titanate ($$K = 300)$$

Question 11

A capacitor is attached to a battery. The plates are then pulled apart so that the distance between them is larger. What happens to the electric field between the plates?

Accepted Answer

The electric field remains constant because the battery maintains the voltage

Question 12

What is the effect of inserting a dielectric into a capacitor that is connected to a battery?

Accepted Answer

The capacitance increases, the charge increases, and the energy stored increases

Question 13

Which equation correctly defines capacitance for a parallel plate capacitor?

Accepted Answer

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

Question 14

A capacitor stores energy in its electric field. Which formula gives the energy density in the field?

Accepted Answer

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

Question 15

A capacitor is used in a timing device, such as windshield wipers. Which property of capacitors makes them suitable for this application?

Accepted Answer

Their ability to rapidly charge and discharge

Question 16

If a capacitor is charged to a voltage $$\Delta V$$ and then disconnected from the battery, what happens to the voltage across the plates if a dielectric is inserted?

Accepted Answer

The voltage decreases because the capacitance increases and the charge remains constant

Question 17

Which of the following is NOT a typical use of capacitors in electronic circuits?

Accepted Answer

Converting electrical energy directly into mechanical energy

Question 18

A capacitor is charged to a voltage $$\Delta V$$ and then disconnected from the battery. If the plates are pulled apart, what happens to the voltage across the plates?

Accepted Answer

The voltage increases because the capacitance decreases and the charge remains constant

Capacitors, Energy Storage, and Dielectrics

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