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 = 10 RC .

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Quantrex Academy · Accepted Answer

Correct answer: D. - i_0 RCe^ 10

The electric current in the circuit is given by

i = i_0 e^{-t/RC}

.

The rate of change of current is obtained by differentiating

i

with respect to time

t

:

\dfrac{di}{dt} = \dfrac{d}{dt} \left( i_0 e^{-t/RC} \right) = i_0 e^{-t/RC} \left( -\dfrac{1}{RC} \right) = -\dfrac{i_0}{RC} e^{-t/RC}

Substituting

t = 10RC

into the expression:

\dfrac{di}{dt} = -\dfrac{i_0}{RC} e^{-10RC/RC} = -\dfrac{i_0}{RC} e^{-10} = -\dfrac{i_0}{RCe^{10}}

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

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