Chapter 18.2 Review

Capacitance and Potential

1. A 5 μF capacitor is connected to a 12 volt battery. What is the potential difference across the plates of the capacitor when it is fully charged?

12 volts, a charged capacitor has the same potential difference across the plates as the source.

2. What is the charge on one plate of the capacitor in problem 1 when it is fully charged? What is the net charge on the capacitor when it is fully charged?

q = VCq = 12 x 5 = 60 μCor

q = 12(5 x 10-6)= 6 x 10-5 C

But the net charge on a capacitor is always zero because the + and – plate have charges of equal magnitude.

3. How much electrical potential energy is stored in the capacitor in problem 1?

PEE = ½ CV2

PEE = ½ 5(12)2

PEE = 360 μJor,PEE = ½ (5x 10-6)(12)2

PEE = 3.6 x 10-4 J

4. If the plates are separated by a distance of 0.003 m, what is the strength of the electric field across the plates?

Ed = VE(0.003) = 12E = 4000 N/C

5. A 9 μF capacitor is connected to a 9 volt battery. What is the potential difference across the plates of the capacitor when it is fully charged?

9 volts, a charged capacitor has the same potential difference across the plates as the source.

6. What is the charge on one plate of the capacitor in problem 5 when it is fully charged? What is the net charge on the capacitor when it is fully charged?

q = VCq = 9 x 9 = 81 μCor

q = 9(9 x 10-6)= 8.1 x 10-5 C

But the net charge on a capacitor is always zero because the + and – plate have charges of equal magnitude.

7. How much electrical potential energy is stored in the capacitor in problem 5?

PEE = ½ CV2

PEE = ½ 9(9)2

PEE = 364.5 μJor,PEE = ½ (9 x 10-6)(9)2

PEE = 3.645 x 10-4 J

8. If the plates are separated by a distance of 0.005 m, what is the strength of the electric field across the plates?

Ed = VE(0.005) = 9E = 1800 N/C

9. List four ways to increase the charge on a capacitor.

1. Larger plates2. Plates closer

together3. Different dielectric4. Increase voltage

10. What is the difference in electrical potential energy and electric potential?

Electric potential is electric potential energy divided by charge.

11. A proton is moved 0.5 m in the direction of an electric field with a strength of 5000 N/C. What is the change in electric potential?

Ed = V5000 x 0.5 = V2500 V = VMoving in the direction of the field is a decrease of potential, so

-2500 V = V.

12. What is the change in electrical potential energy of the proton in problem 11?

PEE = qV

PEE = (1.6 x 10-19)(2500)

PEE = -4 x 10-16 J

13. An electron is moved 0.8 m in the direction of an electric field with a strength of 3000 N/C. What is the change in electric potential?

Ed = V3000 x 0.8 = V2400 V = VMoving in the direction of the field is a decrease of potential, so

-2400 V = V.

14. What is the change in electrical potential energy of the electron in problem 13?

PEE = qV

PEE = (-1.6 x 10-19)(-2400)

PEE = 3.88 x 10-16 J

The electron is being moved in the direction it does not “want” to go. That is an increase in potential energy.

15. A helium nucleus (composed of two protons and two neutrons) is moved 24 cm in the direction of an electric field with a strength of 9000 N/C. What is the change in electric potential?

Ed = V9000 x 0.24 = V2160 V = VMoving in the direction of the field is a decrease of potential, so

-2160 V = V.

16. What is the change in electrical potential energy of the helium nucleus in problem 15?

PEE = qV

PEE = (1.6 x 10-19)(2)(-2160)(There are two protons in one helium nucleus.)

PEE = -6.912 x 10-16