Question

In the series LCR circuit shown the impedance is

• A. 200$\Omega$
• B. 100$\Omega$
• C. 300$\Omega$
• D. 500$\Omega$

Answer 1

Answer: (D)

500$\Omega$

Answer 2

: Here, , $L = 1H,C = 20\mu F = 20 \times 10^{- 6}F$

$R = 300\Omega,\upsilon = \frac{50}{\pi}Hz.$

The inductive reactance is,

$X_{L} = 2\pi\upsilon L = 2 \times \pi \times \frac{50}{\pi} \times 1 = 100\Omega$

The capacitive reactance is,

$X_{C} = \frac{1}{2\pi\upsilon C} = \frac{1}{2 \times \pi \times \frac{50}{\pi} \times 20 \times 10^{- 6}} = 500\Omega$

The impedance of the series LCR circuit is,

$Z = \sqrt{R^{2} + (X_{C} - X_{L})^{2}}$

$= \sqrt{(300)^{2} + (500 - 100)^{2}}$

$= \sqrt{(300)^{2} + (400)^{2}} = 500\Omega$