To light, a 50 ~W, 100 ~V lamp is connected, in series with a capacitor of capacitance 50/(π √(x)) μ F, with 200 ~V, 50 ~Hz AC source. The value of x will be _ _ _ _ _ _.

Electromagnetic Induction and Alternating Currents: JEE Main 2022 Physics question

JEE Main 2022 · 27 Jul, Morning shift · Q56

JEE Main 202227 Jul, Morning shiftPhysicsMediumElectromagnetic Induction and Alternating Currents149× since 2002

To light, a

50 \mathrm{~W}, 100 \mathrm{~V}

lamp is connected, in series with a capacitor of capacitance

\frac{50}{\pi \sqrt{x}} \mu F

, with

200 \mathrm{~V}, 50 \mathrm{~Hz} \,\mathrm{AC}

source. The value of

x

will be ___________.

Your answerType your answer. Integers and decimals are accepted.