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BITSAT 2023Paper 2
Exam
BITSAT
Year
2023
Paper
Paper 2
Subject
Physics
Chapter
Alternating Current

BITSAT 2023 · Paper 2 · Physics · Alternating Current

In the given circuit, rms value of current (Irms) through the...

In the given circuit, rms value of current (Irms) through the resistor RR is :
In the given circuit, rms value of current (Irms) through the resistor R is :

Options

  1. A2A2 \mathrm{ A}
  2. B12A\frac{1}{2} \mathrm{ A}
  3. C20A20 \mathrm{ A}
  4. D22A2 \sqrt{2} \mathrm{ A}

Correct answer

A. 2A2 \mathrm{ A}

Step-by-step solution

(a) Given,
Capacitive reactance, XC=100Ω\mathrm{X}_{\mathrm{C}}=100 \Omega
Inductive reactance, XL=200Ω\mathrm{X}_{\mathrm{L}}=200 \Omega
Resistance, R=100ΩR=100 \Omega
Impedance, Z=R2+(XL−XC)2\mathrm{Z}=\sqrt{\mathrm{R}^2+\left(\mathrm{X}_{\mathrm{L}}-\mathrm{X}_{\mathrm{C}}\right)^2}
Z=1002+(200−100)2=1002ΩZ=\sqrt{100^2+(200-100)^2}=100 \sqrt{2} \Omega
RMS value of current,
irms=VrmsZ=20021002=2Ai_{\mathrm{rms}}=\frac{V_{\mathrm{rms}}}{Z}=\frac{200 \sqrt{2}}{100 \sqrt{2}}=2 \mathrm{ A}
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