An inductor of 10 mH, capacitor of 0.1 and a resistor of 100 Ω are… | JEE Main 2026 (4 Apr, Shift 1)

Q16JEE Main 2026 · 4 APR · SHIFT 1Medium

Power, Power Factor & Wattless Current

An inductor of 10 mH, capacitor of $0.1\ \mu\text{F}$ and a resistor of $100\ \Omega$ are connected in series across an $a.c$ power supply $220\text{ V}, 70\text{ Hz}$ . The power factor of the given circuit is 0.5. The difference in the inductive reactance and capacitance reactance is $\sqrt{3}\alpha\ \Omega$ . The value of $\alpha$ is ______.

Numerical answer type. Work it out, then open the answer.

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Answer: 100

$\cos\phi = 0.5 \Rightarrow \phi = 60^\circ$
$\tan\phi = \frac{X_L - X_C}{R} = \sqrt{3}$
$|X_L - X_C| = \sqrt{3}\times 100 = 100\sqrt{3}\ \Omega$
So $\alpha = 100$ .

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Power, Power Factor & Wattless Current question from JEE Main 2026 (4 Apr, Shift 1)

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