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If $Z_1$ and $Z_2$ are the impedances of the given circuits (a) and (b) as shown in figures, then choose the correct option.
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Verified Answer
The correct answer is:
$Z_1 < Z_2$
$Z_1=R=10 \Omega$ [as, D.C. voltage is supplied]
$Z_2=\sqrt{R^2+\left(X_C\right)^2}=\sqrt{(10)^2+\left[\frac{1}{2 \times \pi \times 50 \times \frac{10^3}{\pi} \times 10^{-6}}\right]^2}$
$\begin{aligned} & \Rightarrow Z_2=\sqrt{(10)^2+(10)^2}=10 \sqrt{2} \\ & \Rightarrow Z_2>Z_1 \text { or } Z_1 < Z_2\end{aligned}$
$Z_2=\sqrt{R^2+\left(X_C\right)^2}=\sqrt{(10)^2+\left[\frac{1}{2 \times \pi \times 50 \times \frac{10^3}{\pi} \times 10^{-6}}\right]^2}$
$\begin{aligned} & \Rightarrow Z_2=\sqrt{(10)^2+(10)^2}=10 \sqrt{2} \\ & \Rightarrow Z_2>Z_1 \text { or } Z_1 < Z_2\end{aligned}$
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