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 𝐢 of the capacitor?

  • A 𝐸 = 2 𝑄 𝐢 
  • B 𝐸 = 𝑄 2 𝐢 
  • C 𝐸 = 𝑄 2 𝐢 
  • D 𝐸 = 𝑄 2 𝐢
  • E 𝐸 = 2 𝑄 𝐢

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?

  • A 𝐸 = 1 2 𝑄 𝑉
  • B 𝐸 = 1 2 𝑄 𝑉 
  • C 𝐸 = 1 2 𝑄 𝑉 
  • D 𝐸 = 2 𝑄 𝑉
  • E 𝐸 = 𝑄 𝑉 

Q3:

A 415 nF capacitor stores 162 Β΅C 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?

  • A 6 . 7 Γ— 1 0    C2/Nβ‹…m2
  • B 3 . 0 Γ— 1 0    C2/Nβ‹…m2
  • C 1 . 7 Γ— 1 0    C2/Nβ‹…m2
  • D 3 . 3 Γ— 1 0    C2/Nβ‹…m2
  • E 9 . 5 Γ— 1 0    C2/Nβ‹…m2

Q5:

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

  • A 8 . 0 Γ— 1 0   C
  • B 1 . 0 Γ— 1 0   C
  • C 5 . 0 Γ— 1 0   C
  • D 2 . 5 Γ— 1 0   C
  • E 1 . 0 Γ— 1 0   C

Q6:

An engineer proposes powering a 60 W light bulb used in a home using a capacitor. The bulb needs to operate for 2 1 Γ— 1 0  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 . 8 5 Γ— 1 0    C/Nβ‹…m2. Find the side length of the plates.

  • A 3 . 5 Γ— 1 0  m
  • B 1 4 Γ— 1 0 οŠͺ m
  • C 7 . 0 Γ— 1 0  m
  • D 7 . 0 Γ— 1 0 οŠͺ m
  • E 3 . 5 Γ— 1 0 οŠͺ 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 Γ— 1 0    C2/Nβ‹…m2. There is a potential difference of 150 V across the plates. How much electrical potential energy is stored in the capacitor?

  • A 6 . 1 Γ— 1 0   J
  • B 1 . 2 Γ— 1 0  οŠͺ J
  • C 4 . 3 Γ— 1 0   J
  • D 3 . 1 Γ— 1 0   J
  • E 8 . 6 Γ— 1 0   J

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