At t = 0 , the plates of a capacitor of capacitance 10 ext , charged to 60 ext , are connected together by a wire having a resistance of 10 ext . Determine the charge on the capacitor in the circuit at t = 30 ext .

Question

Quantrex Academy · Accepted Answer

Correct answer: B. 44 ext

The time constant of the discharging RC circuit is given by

\tau = RC

.

Substituting the given values:

\tau = 10 \times 10 \times 10^{-6} \text{ s} = 100 \mu\text{s}

The charge on the capacitor during discharging is given by:

q = q_0 e^{-t/\tau}

Substituting

q_0 = 60 \mu\text{C}

and

t = 30 \mu\text{s}

:

q = 60 e^{-30/100} = 60 e^{-0.3} \mu\text{C}

Using the approximation

e^{-0.3} \approx 0.74

:

q \approx 60 \times 0.74 \mu\text{C} = 44.4 \mu\text{C}

The closest value among the given options is

44 \mu\text{C}

.

At t = 0 , the plates of a capacitor of capacitance 10 ext ,...

Options

Correct answer

Step-by-step solution

More from Electric Current in Conductors