JEE Main 2022 · 27 Jul · Shift 1 · Physics Q54

← JEE Main 2022 · 27 Jul · Shift 1

PhysicsInteger+4 / -1Question 54 of 90

To light, a 50 W, 100 V lamp is connected, in series with a capacitor of capacitance $\dfrac{50}{\pi\sqrt x}$ μF, with 200 V, 50 Hz AC source. The value of $x$ will be ______.

Your answer

Answer and worked solution

Official answer: 3

Lamp. $R=\frac{100^2}{50}=200$ Ω, $I=0.5$ A.

Capacitor. $V_C=\sqrt{200^2-100^2}=100\sqrt3$ V, so $X_C=200\sqrt3$ Ω and $C=\frac1{2\pi\cdot50\cdot200\sqrt3}=\frac{50}{\pi\sqrt3}$ μF.

Answer: 3

Topics:Reactance and impedance Power in AC circuits

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JEE Main 2022 · 27 Jul · Shift 1, Physics question 54