Worksheet: Parallel-Plate Capacitors

In this worksheet, we will practice relating the capacitance of parallel-plates to charge, potential difference, and electric field strength.

Q1:

A sweater made of a synthetic material becomes statically charged by friction. The sweater and the skin beneath it act as a 55 nF capacitor. The person wearing the sweater comes into contact with a conducting surface that carries away the charge stored in the capacitor by producing a 220 mV spark.

How much charge was stored in the capacitor?

  • A 5 . 7 × 1 0 C
  • B 1 . 3 × 1 0 C
  • C 3 . 8 × 1 0 C
  • D 1 . 2 × 1 0 C
  • E 2 . 5 × 1 0 C

How many excess electrons were stored by the sweater? Use the value 1 . 6 × 1 0 C for the charge of an electron.

  • A 8 . 1 × 1 0
  • B 2 . 4 × 1 0
  • C 1 . 6 × 1 0
  • D 3 . 6 × 1 0
  • E 7 . 6 × 1 0

Q2:

At the instant when the current through the resistor in the circuit shown in the diagram is 0.69 A, what charge is stored by the 22 µF capacitor in the circuit?

  • A 5 . 6 × 1 0 C
  • B 1 . 2 × 1 0 C
  • C 4 . 3 × 1 0 C
  • D 3 . 3 × 1 0 C
  • E 2 . 1 × 1 0 C

Q3:

Which of the following formulas correctly relates the charge 𝑄 stored by a parallel plate capacitor to the capacitance 𝐶 of the capacitor, the permittivity 𝜀 of the medium between the plates, and the potential difference 𝑉 across the plates?

  • A 𝐶 = 𝑄 𝜀 𝑉
  • B 𝐶 = 𝑉 𝑄
  • C 𝐶 = 𝑄 𝜀 𝑉
  • D 𝐶 = 𝑄 𝑉
  • E 𝐶 = 𝑄 𝑉

Q4:

A parallel plate capacitor has square plates with sides 20 cm long, 7.5 mm apart. The potential difference across the plates is 35 V and the permittivity of the space between the plates is 8 . 8 5 × 1 0 C2/N⋅m2. What is the charge stored by the capacitor?

  • A 1 . 7 × 1 0 C
  • B 2 . 8 × 1 0 C
  • C 3 . 5 × 1 0 C
  • D 1 . 3 × 1 0 C
  • E 6 . 7 × 1 0 C

Q5:

The capacitor in the circuit shown in the diagram stores a charge of 3.6 mC. What is the potential difference V across the resistor?

Q6:

An 11.5 µF parallel plate capacitor stores 888 µC of charge. What is the potential difference across its plates?

  • A 97.9 V
  • B 77.2 V
  • C 14.6 V
  • D 6.71 V
  • E 88.8 V

Q7:

A 475 µF parallel plate capacitor has a potential difference of 12.5 V across its plates. What charge does the capacitor store?

  • A 5.94 mC
  • B 22.5 mC
  • C 3.04 µC
  • D 74.2 mC
  • E 38.0 µC

Q8:

A parallel-plate capacitor has square plates with sides 15 cm long, 2.5 cm apart. Find the capacitance of the capacitor. Use the value 8 . 8 5 × 1 0 C/N⋅m2 for the permittivity of the space between the plates, and answer to two significant figures.

  • A 8 . 0 × 1 0 F
  • B 6 . 2 × 1 0 F
  • C 1 . 5 × 1 0 F
  • D 9 . 8 × 1 0 F
  • E 5 . 3 × 1 0 F

Q9:

The capacitor in the circuit shown in the diagram stores a charge of 160 µC. What is the capacitance of the capacitor?

Q10:

A 2.1 nF parallel plate capacitor has square plates with sides 25 cm long, 1.5 cm apart. Find the permittivity of the space between the plates.

  • A 1 . 9 × 1 0 C2/N⋅m2
  • B 1 . 3 × 1 0 C2/N⋅m2
  • C 2 . 3 × 1 0 C2/N⋅m2
  • D 5 . 0 × 1 0 C2/N⋅m2
  • E 4 . 5 × 1 0 C2/N⋅m2

Q11:

A parallel plate capacitor has square plates with a 1.25 V/m uniform electric field between them. The permittivity of the space between the plates is 1 . 1 0 × 1 0 C2/N⋅m2. What is the charge density of the plates?

  • A 8 . 8 0 × 1 0 C/m2
  • B 6 . 8 8 × 1 0 C/m2
  • C 2 . 7 5 × 1 0 C/m2
  • D 4 . 3 0 × 1 0 C/m2
  • E 1 . 3 8 × 1 0 C/m2

Q12:

A 36 µF parallel plate capacitor stores 240 µC of charge. There is a uniform electric field between the plates of the capacitor. The plates are 6.5 cm apart. What is the strength of the electric field?

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