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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 charging R – C circuit, the electric current is given by i =...

In a charging

R

–

C

circuit, the electric current is given by

i = i_0 e^{-t/RC}

, where

i_0

,

R

, and

C

are constant parameters of the circuit and

t

represents time. Determine the rate of change of current at

t = RC

.

Options

A $-\dfrac{i_0 e}{RC}$
B $-\dfrac{i_0}{RCe}$
C $\dfrac{i_0}{RCe}$
D $-\dfrac{i_0}{RC}$

Correct answer

B. $-\dfrac{i_0}{RCe}$

Step-by-step solution

Given the electric current

i = i_0 e^{-t/RC}

.

The rate of change of current is given by

\dfrac{di}{dt}

.

Differentiating

i

with respect to

t

gives:

\dfrac{di}{dt} = \dfrac{d}{dt} (i_0 e^{-t/RC}) = -\dfrac{i_0}{RC} e^{-t/RC}

Substituting

t = RC

into the expression:

\dfrac{di}{dt} = -\dfrac{i_0}{RC} e^{-RC/RC} = -\dfrac{i_0}{RC} e^{-1} = -\dfrac{i_0}{RCe}

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