If $Z_1$ and $Z_2$ are the impedances of the given circuits (a) and (b) as shown in figures, then choose the…

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.
  1. $Z_1=Z_2$
  2. $Z_1>Z_2$
  3. $Z_1 < Z_2$
  4. $Z_1+Z_2=20 \Omega$

Solution

$Z_1=R=10 \Omega$ [as, D.C. voltage is supplied] $Z_2=\sqrt{R^2+\left(X_C\right)^2}=\sqrt{(10)^2+\left[\frac{1}{2 \times \pi \times 50 \times \frac{10^3}{\pi} \times 10^{-6}}\right]^2}$ $\begin{aligned} & \Rightarrow Z_2=\sqrt{(10)^2+(10)^2}=10 \sqrt{2} \\ & \Rightarrow Z_2>Z_1 \text { or } Z_1 < Z_2\end{aligned}$

Asked in: NEET 2023 (Manipur)

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