JEE Main 2026 Apr 4 Shift 1, Physics Q25: LR, CR, LCR Circuits

JEE Main2026Apr 4, Shift 1Physics

An inductor of $10$ mH, capacitor of $0.1 μ$ F and a resistor of $100 Ω$ are connected in series across an a.c power supply $220$ V, $70$ Hz. The power factor of the given circuit is $0.5$ . The difference in the inductive reactance and capacitance reactance is $3 α Ω$ . The value of $α$ is _______.

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Solution

For a series LCR circuit, $cos ϕ = \frac{R}{Z}$ and $tan ϕ = \frac{∣ X _{L} - X _{C} ∣}{R} .$

Given $cos ϕ = 0.5 = \frac{1}{2} \Rightarrow ϕ = 6 0^{\circ} \Rightarrow tan ϕ = 3 .$

$∣ X_{L} - X_{C} ∣ = R tan ϕ = 1003 Ω.$

Equate with $3 α$ : $3 α = 1003 \Rightarrow α = 100.$

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JEE Main 2026 Apr 4 Shift 1, Physics Q25: LR, CR, LCR Circuits

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