Question

A real battery with internal resistance 0.460 Ω and emf 9.00 V is used to charge a 56.0-µF capacitor. A 21.0-Ω resistor is put in series with the battery and the capacitor when charging. (a) What is the time constant for this circuit?

Answer 1

Given Information:

Internal resistance of battery = 0.460

Resistance = 21.0 Ω

Capacitance = 56.0 µF

Required Information:

time constant = τ = ?

Answer:

τ = 0.0012

Explanation:

The time constant τ provides the information about how long it will take to charge the capacitor up to certain level.

τ = Req*C

Where Req is the equivalent resistance and C is the capacitance.

Req = R + r

Where R is the resistance of the resistor and r is the internal resistance of the battery.

Req = 21.0 + 0.460 = 21.460 Ω

τ = Req*C

τ = 21.46*56x10⁻⁶

τ = 0.0012

A capacitor approximately charges to 63% in one τ and about 99% in 5τ

Answer 2

Answer: 1.176×10^-3 s

Explanation: The time constant formulae for an RC circuit is given below as

t =RC

Where t = time constant , R = magnitude of resistance = 21 ohms , C = capacitance of capacitor = 56 uf = 56×10^-6 F

t = 56×10^-6 × 21

t = 1176×10^-6

t = 1.176×10^-3 s