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Concepts Of Physics MCQ Edition [Volume 1]

Exam: Concepts Of Physics MCQ Edition [Volume 1]
Subject: Physics
Chapter: Physics and Mathematics

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Physics and Mathematics

In a discharging R – C circuit, the electric current is given by i...

In a discharging

R

–

C

circuit, the electric current is given by

i = i_0 e^{-t/RC}

, where

i_0

,

R

and

C

denote constant parameters and

t

represents time. If

i_0 = 2.00 \text{ A}

,

R = 6.00 \times 10^5 \Omega

and

C = 0.500 \mu\text{F}

, determine the current at

t = 0.3 \text{ s}

.

Options

A $\dfrac{1.00}{e} \text{ A}$
B $2.00e \text{ A}$
C $\dfrac{2.00}{e^2} \text{ A}$
D $\dfrac{2.00}{e} \text{ A}$

Correct answer

D. $\dfrac{2.00}{e} \text{ A}$

Step-by-step solution

Given parameters are

i_0 = 2.00 \text{ A}

,

R = 6.00 \times 10^5 \Omega

,

C = 0.500 \times 10^{-6} \text{ F}

, and

t = 0.3 \text{ s}

.

The time constant of the circuit is calculated as:

RC = (6.00 \times 10^5) \times (0.500 \times 10^{-6}) = 3.00 \times 10^{-1} \text{ s} = 0.3 \text{ s}

The current at time

t

is given by the equation:

i = i_0 e^{-t/RC}

Substituting the values into the equation:

i = 2.00 \times e^{-0.3/0.3}

i = 2.00 \times e^{-1} = \dfrac{2.00}{e} \text{ A}

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