Question

The net impedance of circuit (as shown in figure) will be ______.

Options

• 15 Ω

• 5\[\sqrt 5\] Ω

• 25 Ω

• 10\[\sqrt 2\] Ω

Answer 1

The net impedance of circuit (as shown in figure) will be 5\[\sqrt 5\] Ω.

Explanation:

Z = \[\sqrt{R^2+\left(X_C-X_L\right)^2}\]

R = 10 Ω

\[X_C=\frac{1}{\omega C}=\frac{1\times10^6}{2\pi(50)\times\frac{10^3}{\pi}}\]

= 10 Ω

X_L = ωL

= \[2\pi(50)\times\frac{50}{\pi}\times10^{-3}\]

= 5 Ω

So Z = \[\sqrt{10^2+\left(10-5\right)^2}\]

= \[\sqrt {125}\]

= 5 \[\sqrt 5\] Ω (where symbols have their usual meanings.)