Question:
A resistor of resistance R, capacitor of capacitance C and inductor of inductance L are connected in parallel to an AC power source of voltage varepsilon₀sinω t. The maximum current through the resistance is half of the maximum current through the power source. Then value of R is:
A resistor of resistance R, capacitor of capacitance C and inductor of inductance L are connected in parallel to an AC power source of voltage varepsilon₀sinω t. The maximum current through the resistance is half of the maximum current through the power source. Then value of R is:
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In parallel AC circuits:
I=√(IR²+(IC-IL)²)
Always compare vector currents, not algebraic sums.
Updated On: Mar 19, 2026
- \(\sqrt{3}\left|\omega C-\dfrac{1}{\omega L}\right|\)
- \(\sqrt{3}\left|\dfrac{1}{\omega C}-\omega L\right|\)
- \(\sqrt{5}\left|\dfrac{1}{\omega C}-\omega L\right|\)
- None of these
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The Correct Option is B
Solution and Explanation
Step 1: In a parallel RLC circuit, the current through the resistor: IR=(V₀)/(R)
Step 2: Net source current: I=√(IR²+(IC-IL)²)
Step 3: Given IR=(I)/(2): I²=4IR² ⟹ (IC-IL)²=3IR²
Step 4: IC-IL=V₀(ω C-(1)/(ω L))
Step 5: (V₀)/(R)=\frac1√(3)V₀|ω C-(1)/(ω L)| ⟹ R=√(3)|(1)/(ω C)-ω L|
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