Question

In the series LCR circuit shown in figure the impedance is

• A. \(300\,\Omega\)
• B. \(500\,\Omega\)
• C. \(700\,\Omega\)
• D. \(900\,\Omega\)

Hint:

Find omega from the frequency, then XL and XC, then Z = sqrt(R^2 + (XL - XC)^2).

Answer 1

The Correct Option is B

Step 1: Phasor triangle:
The reactances act at right angles to the resistance. The net reactance is $|X_L - X_C|$.

Step 2: Numbers:
$\omega = 100$ rad/s, so $X_L = 100\ \Omega$ and $X_C = \dfrac{1}{100\times20\times10^{-6}} = 500\ \Omega$. The net reactance is $400\ \Omega$.

Step 3: Right triangle:
The sides are 300 and 400, so the hypotenuse is 500. This is the familiar 3-4-5 triangle scaled by 100.

Final Answer:
$Z = 500\ \Omega$, option (B). \[ \boxed{500\ \Omega \text{ (B)}} \]