Question

In the given circuit, r.m.s. value of current through the resistor \(R\) is

• A. \(20\) A
• B. \(2\) A
• C. \(0.5\) A
• D. \(2\sqrt{2}\) A

Hint:

Impedance is the square root of R squared plus the square of X_L minus X_C; divide the r.m.s. voltage by it.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
In a series LCR circuit the same current flows through every element. \(Z=\sqrt{R^{2}+(X_{L}-X_{C})^{2}}\).

Step 2: Impedance
\(X_{L}-X_{C}=200-100=100\,\Omega\)
\(Z=\sqrt{100^{2}+100^{2}}=100\sqrt{2}\,\Omega\)

Step 3: Calculation
\(I_{rms}=\frac{V_{rms}}{Z}=\frac{200\sqrt{2}}{100\sqrt{2}}=2\) A

Step 4: Compare the options
This is option (B).

Final Answer:
The r.m.s. current through the resistor is 2 A. \[ \boxed{\text{(B) }2\ \text{A}} \]