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Concepts Of Physics MCQ Edition [Volume 2]

Exam: Concepts Of Physics MCQ Edition [Volume 2]
Subject: Physics
Chapter: Electric Current in Conductors

Concepts Of Physics MCQ Edition [Volume 2] · Physics · Electric Current in Conductors

A 10 capacitor is connected to a battery with an emf of 2 V . It...

A

10 \mu\text{F}

capacitor is connected to a battery with an emf of

2 \text{ V}

. It takes

50 \text{ ms}

for the charge on the capacitor to reach

12.6 \mu\text{C}

. Determine the resistance of the circuit.

Options

A $5 \Omega$
B $2.5 \text{ k}\Omega$
C $5 \text{ k}\Omega$
D $10 \text{ k}\Omega$

Correct answer

C. $5 \text{ k}\Omega$

Step-by-step solution

Given

C = 10 \mu\text{F}

,

V = 2 \text{ V}

,

t = 50 \text{ ms}

, and

q = 12.6 \mu\text{C}

.

The maximum charge on the capacitor is

q_0 = CV = 10 \times 10^{-6} \times 2 = 20 \mu\text{C}

.

The charge on a capacitor during charging is given by

q = q_0(1 - e^{-t/RC})

.

Substituting the values:

12.6 = 20(1 - e^{-t/RC})

1 - e^{-t/RC} = \dfrac{12.6}{20} = 0.63

e^{-t/RC} = 0.37

Since

e^{-1} \approx 0.37

, we have

\dfrac{t}{RC} = 1

.

Therefore,

RC = t = 50 \text{ ms}

.

R = \dfrac{50 \times 10^{-3}}{10 \times 10^{-6}} = 5 \times 10^3 \Omega = 5 \text{ k}\Omega

.

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