Q83 / 100 · BITSAT 2023 (Memory Based Paper 2) · Physics
In the given circuit, rms value of current (Irms) through the resistor $R$ is :
- Correct answerA$2 \mathrm{~A}$
- B$\frac{1}{2} \mathrm{~A}$
- C$20 \mathrm{~A}$
- D$2 \sqrt{2} \mathrm{~A}$
Solution
(a) Given,
Capacitive reactance, $\mathrm{X}_{\mathrm{C}}=100 \Omega$
Inductive reactance, $\mathrm{X}_{\mathrm{L}}=200 \Omega$
Resistance, $R=100 \Omega$
Impedance, $\mathrm{Z}=\sqrt{\mathrm{R}^2+\left(\mathrm{X}_{\mathrm{L}}-\mathrm{X}_{\mathrm{C}}\right)^2}$
$Z=\sqrt{100^2+(200-100)^2}=100 \sqrt{2} \Omega$
RMS value of current,
$i_{\mathrm{rms}}=\frac{V_{\mathrm{rms}}}{Z}=\frac{200 \sqrt{2}}{100 \sqrt{2}}=2 \mathrm{~A}$
Capacitive reactance, $\mathrm{X}_{\mathrm{C}}=100 \Omega$
Inductive reactance, $\mathrm{X}_{\mathrm{L}}=200 \Omega$
Resistance, $R=100 \Omega$
Impedance, $\mathrm{Z}=\sqrt{\mathrm{R}^2+\left(\mathrm{X}_{\mathrm{L}}-\mathrm{X}_{\mathrm{C}}\right)^2}$
$Z=\sqrt{100^2+(200-100)^2}=100 \sqrt{2} \Omega$
RMS value of current,
$i_{\mathrm{rms}}=\frac{V_{\mathrm{rms}}}{Z}=\frac{200 \sqrt{2}}{100 \sqrt{2}}=2 \mathrm{~A}$
Hence, the correct answer is option: 'A'.