Question

In the given circuit, rms value of current $\left( I _{ rms }\right)$ through the resistor $R$ is:

• A. $\frac{1}{2} A$
• B. $20 A$
• C. $2 A$
• D. $2 \sqrt{2} A$

Answer 1

The Correct Option is C

To find the rms value of the current through the resistor \( R \), we need to understand the given RLC series circuit and use the formula for current in an AC circuit.

The components of the circuit are:

• Inductive Reactance, \( X_L = 200 \, \Omega \)
• Capacitive Reactance, \( X_C = 100 \, \Omega \)
• Resistance, \( R = 100 \, \Omega \)
• RMS Voltage, \( V_{rms} = 200 \sqrt{2} \, V \)

Step 1: Calculate the net reactance \( X \) of the circuit:

\(X = X_L - X_C\)

Substituting the given values:

\(X = 200 \, \Omega - 100 \, \Omega = 100 \, \Omega\)

Step 2: Calculate the impedance \( Z \) of the circuit using the formula:

\(Z = \sqrt{R^2 + X^2}\)

Substitute the values:

\(Z = \sqrt{(100 \, \Omega)^2 + (100 \, \Omega)^2} = \sqrt{10000 + 10000} = \sqrt{20000} = 100 \sqrt{2} \, \Omega\)

Step 3: Calculate the rms current \( I_{rms} \) using Ohm's Law for AC circuits:

\(I_{rms} = \frac{V_{rms}}{Z}\)

Substitute the known values:

\(I_{rms} = \frac{200 \sqrt+2}{100 \sqrt{2}} = 2 \, A\)

Conclusion: The rms value of the current through the resistor \( R \) is \( 2 \, A \). Thus, the correct option is \( 2 \, A \).