Question

A 100 μF capacitor is joined to a 24 V battery through a 1.0 MΩ resistor. Plot qualitative graphs (a) between current and time for the first 10 minutes and (b) between charge and time for the same period.

Answer 1

Explanation:

The circuit’s time constant,

τ = RC

= 1 × 106 × 100 × 10−6

= 100 s

The capacitor’s charge of growth,

q = VC (1 − e-tRC)

Via the circuit, the current,

i = dqdt = VR. e-tRC = 24 × 10-6• e-t100

For t = 10 min = 600 s

q = 23.99 × 10−4

i = 24106.1e = 5.9 × 10-8 A

(a) The plot among time and current for the first 10 minutes.

(b) The below graph shows the plot between time and charge for the first 10 minutes.