Worksheet: Energy Stored in Capacitors

In this worksheet, we will practice relating the capacitance of and voltage across parallel-plate capacitors to the charge and energy stored in them.

Q1:

Which of the following formulas correctly relates the energy 𝐸 stored by a parallel plate capacitor to the charge 𝑄 stored by the capacitor and the capacitance 𝐶 of the capacitor?

  • A𝐸=𝑄2𝐶
  • B𝐸=𝑄2𝐶
  • C𝐸=2𝑄𝐶
  • D𝐸=2𝑄𝐶
  • E𝐸=𝑄2𝐶

Q2:

Which of the following formulas correctly relates the energy 𝐸 stored by a parallel plate capacitor to the charge 𝑄 stored by the capacitor and the potential difference 𝑉 across the plates?

  • A𝐸=12𝑄𝑉
  • B𝐸=𝑄𝑉
  • C𝐸=2𝑄𝑉
  • D𝐸=12𝑄𝑉
  • E𝐸=12𝑄𝑉

Q3:

A 415 nF capacitor stores 162 µC of charge. How much electrical potential energy is stored in the capacitor?

Q4:

A very large capacitor has plates with areas of 1.5 m2 that are 1.2 mm apart. What would the permittivity of the space between the plates need to be for the capacitor to store 2.5 mC of charge and 150 J of electrical potential energy?

  • A9.5×10 C2/N⋅m2
  • B1.7×10 C2/N⋅m2
  • C6.7×10 C2/N⋅m2
  • D3.0×10 C2/N⋅m2
  • E3.3×10 C2/N⋅m2

Q5:

A capacitor has a potential difference of 48 V across its plates. The capacitor stores 120 µJ of electrical potential energy. How much charge is stored on a plate of the capacitor?

  • A8.0×10 C
  • B5.0×10 C
  • C1.0×10 C
  • D2.5×10 C
  • E1.0×10 C

Q6:

An engineer proposes powering a 60 W light bulb used in a home using a capacitor. The bulb needs to operate for 21×10 s before recharging. The capacitor would be charged by a 120 V source.

What would the capacitance of the capacitor need to be to power the light bulb?

The capacitor that powers the bulb would have square plates 0.25 mm apart. The space between the plates would have a permittivity of 8.85×10 C/N⋅m2. Find the side length of the plates.

  • A7.0×10 m
  • B7.0×10 m
  • C3.5×10 m
  • D3.5×10 m
  • E14×10 m

Q7:

A capacitor has plates with areas of 0.15 m2 that are 5.5 mm apart. The permittivity of the space between the plates is 1.4×10 C2/N⋅m2. There is a potential difference of 150 V across the plates. How much electrical potential energy is stored in the capacitor?

  • A6.1×10 J
  • B3.1×10 J
  • C1.2×10 J
  • D8.6×10 J
  • E4.3×10 J

Q8:

A capacitor has a potential difference of 148 V across its plates. The capacitor stores 3.85 µC of charge. How much electrical potential energy is stored per excess electron on the capacitor’s negatively charged plate? Use 1.60×10 C for the value of electron charge. Answer to three significant figures.

  • A5.95×10 J
  • B1.18×10 J
  • C1.28×10 J
  • D4.72×10 J
  • E2.36×10 J

Q9:

Which of the following formulas correctly relates the energy 𝐸 stored by a parallel plate capacitor to the capacitance 𝐶 of the capacitor and the potential difference 𝑉 across the plates?

  • A𝐸=𝐶𝑉
  • B𝐸=12𝐶𝑉
  • C𝐸=2𝐶𝑉
  • D𝐸=12𝐶𝑉
  • E𝐸=12𝐶𝑉

Q10:

A 660 nF capacitor has a potential difference of 240 V across its plates. How much electrical potential energy is stored in the capacitor?

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