Capacitors

Question 1

Define Capacitance

Answer 1

The capacitance of an object is the amount of charge it is able to store per unit potential difference

Question 2

Capacitance calculation 1

Answer 2

C = Q/V

Question 3

Capacitance calculation 2

Answer 3

𝐶 = 𝐴𝜀₀𝜀ᵣ/d

Question 4

Energy stored on a capacitor

Answer 4

E = 1/2QV = 1/2CV² = 1/2Q²/C

Question 5

Relative permittivity of a material

Answer 5

𝜀ᵣ = 𝜀₁/𝜀₀

Question 6

Charge on a charging capacitor

Answer 6

Q = Q₀(1 - e⁻ᵗ/ʳᶜ)

Question 7

Voltage across a charging capacitor

Answer 7

V = V₀(1 - e⁻ᵗ/ʳᶜ)

Question 8

Current across a charging capacitor

Answer 8

I = I₀e₀

Question 9

Charge left on the plates after discharging

Answer 9

Q = Q₀e⁻ᵗ/ʳᶜ

Question 10

Voltage on a discharged capacitor

Answer 10

V = V₀e⁻ᵗ/ʳᶜ

Question 11

Current on a discharged capacitor

Answer 11

I = I₀e⁻ᵗ/ʳᶜ

Question 12

Time taken to halve

Answer 12

1. Q = 1/2Q₀
2. 1/2Q₀ = Q₀e⁻ᵗ/ʳᶜ
3. 1/2 = e⁻ᵗ/ʳᶜ
4. ln(1/2) = ln(e⁻ᵗ/ʳᶜ)
5. ln(2⁻¹) = -ln2 (1/2 can be written as 2⁻¹)
6. -ln(2) = -t/RC (ln(2) = 0.693)
7. t = ln(2)RC
8. T₁/₂ = 0.69RC

Question 13

Time constant

Answer 13

Q = Q₀e⁻¹
Q/Q₀ = 1/e = 0.37

The time constant is the time taken for the charge on a discharging capacitor to fall by 37% and the time taken for the charge on a charging capacitor to rise by 63%