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If $Z_1$ and $Z_2$ are the impedances of the given circuits (a) and (b) as shown in figures (a: 5 mH inductor with 10 $\Omega$ resistor on a 6V DC source; b: $\dfrac{10^3}{\pi}\mu F$ capacitor with 10 $\Omega$ resistor on 220V, 50Hz AC source), then choose the correct option [add image]
A
$Z_1<Z_2$
B
$Z_1+Z_2=20\ \Omega$
C
$Z_1=Z_2$
D
$Z_1>Z_2$
Detailed Solution
For circuit (a), a DC source means $X_L=0$, so $Z_1=\sqrt{X_L^2+R^2}=R=10\ \Omega$. For circuit (b), $X_C=\dfrac{1}{2\pi\times50\times\frac{10^3}{\pi}\times10^{-6}}=10\ \Omega$, so $Z_2=\sqrt{X_C^2+R^2}=\sqrt{10^2+10^2}=10\sqrt2\ \Omega$. Hence $Z_1<Z_2$.