An inductor of 10 mH, capacitor of and a resistor of are connected in series across an a.c. power supply 220 V, 70 Hz

Question

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 $\sqrt{3} α Ω$ . The value of $α$ is ______. [2026]

Smart Achievers · Accepted Answer

(100)

$Given : Resistance = 100 Ω$

$power factor \cos ϕ = \frac{R}{Z} = 0.5$

$Z = \frac{R}{0.5} = 2 R = 2 \times 100 = 200 Ω$

$Now impedance in a series circuit is$

$Z^{2} = R^{2} + {(X_{L} - X_{C})}^{2}$

$40000 = 10000 + {(X_{L} - X_{C})}^{2}$

${(X_{L} - X_{C})}^{2} = 30000$

$| X_{L} - X_{C} |$ $= \sqrt{30000} = 100 \sqrt{3} Ω$

$Now compare it with \sqrt{3} α; we get, α = 100$

Solution

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Solution

Q. An inductor of 10 mH, capacitor of 0.1 μF 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 3α Ω. The value of α is ______. [2026]

Ans. (100) Given : Resistance=100 Ω power factor cosϕ=RZ=0.5 Z=R0.5=2R=2×100=200 Ω Now impedance in a series circuit is Z2=R2+(XL-XC)2 40000=10000+(XL-XC)2 (XL-XC)2=30000 |XL-XC|=30000=1003 Ω Now compare it with 3α; we get, α=100

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