Question 176 of 180

In the given circuits $\left(a\right)$ and $\left(b\right)$, switches ${\text{S}}_{1}$ and ${\text{S}}_{2}$ are closed at $\text{t}=0$ and kept close for a long time. The variation of currents in the two circuits for $\text{t}\geq 0$ are shown in the options. (Figures are schematic and not drawn to scale.)

ABCD

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Answer: (B)

In C-R series circuit,
$\text{q}={\text{q}}_{0}\left(1-{\text{e}}^{\dfrac{-t}{\text{τ}}}\right)$
$⟹\text{q}=\text{CE}\left(1-{\text{e}}^{\dfrac{-\text{t}}{\text{RC}}}\right)$
$∴\text{I}=\dfrac{\text{d}\text{q}}{\text{d}\text{t}}$
$=\dfrac{\text{CE}}{\text{RC}}\left(+{\text{e}}^{\dfrac{-\text{t}}{\text{RC}}}\right)$
$\text{I}=\dfrac{\text{E}}{\text{R}}{\text{e}}^{\dfrac{-\text{t}}{\text{RC}}}$
$⟹$ the urrent decays exponentially. In $L-R$ series circuit,
$\text{I}={\text{I}}_{0}(1-{\text{e}}^{\dfrac{-\text{t}}{\text{τ}}})$
$\Rightarrow {\text{I}}_{0}=\dfrac{\text{E}}{\text{R}}$
$\text{⇒}\text{I}=\dfrac{\text{E}}{\text{R}}\left(1-{\text{e}}^{\dfrac{-\text{Rt}}{\text{L}}}\right)$
$⟹$ current grows exponentially.

$∴$ For $C-R$ circuit,



For $L-R$ circuit,