Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 20245 AprilMorning Shift
Exam
JEE Main
Year
2024
Date
5 April
Shift
Morning Shift
Subject
Physics
Chapter
Alternating Current

JEE Main 2024 · 5 April · Morning Shift · Physics · Alternating Current

An ac source is connected in given series LCR circuit. The rms...

An ac source is connected in given series LCR circuit. The rms potential difference across the capacitor of 20μF20 \mu \mathrm{F} is _____V. An ac source is connected in given series LCR circuit. The rms potential difference across the capacitor of 20 μ F is

Correct answer

0

Step-by-step solution

XL=ωL=100×1=100ΩXC=1ωC=1100×20×10−6=500ΩZ=(XL−XC)2+R2(100−500)2+3002Z=500Ωirms =Vrms Z=50500=0.1A rms voltage across capacitor Vrms =XCirms =500×0.1=50V\begin{aligned} & \mathrm{X}_{\mathrm{L}}=\omega \mathrm{L}=100 \times 1=100 \Omega \\ & \mathrm{X}_{\mathrm{C}}=\frac{1}{\omega \mathrm{C}}=\frac{1}{100 \times 20 \times 10^{-6}}=500 \Omega \\ & \mathrm{Z}=\sqrt{\left(\mathrm{X}_{\mathrm{L}}-\mathrm{X}_{\mathrm{C}}\right)^2+\mathrm{R}^2} \\ & \sqrt{(100-500)^2+300^2} \\ & \mathrm{Z}=500 \Omega \\ & \mathrm{i}_{\text{rms }}=\frac{\mathrm{V}_{\text{rms }}}{\mathrm{Z}}=\frac{50}{500}=0.1 \mathrm{ A} \\ & \text{ rms voltage across capacitor } \\ & \mathrm{V}_{\text{rms }}=\mathrm{X}_{\mathrm{C}} \mathrm{i}_{\text{rms }} \\ & =500 \times 0.1=50 \mathrm{ V}\end{aligned}
Practice Alternating Current on Quantrex Academy →

More from Alternating Current

Consider a circuit consisting of a capacitor of capacitance C and a coil with N turns per… JEE Advanced 2026A LCR series circuit driven with E_ rms = 90 V at frequency f_d = 30 Hz has resistance R… JEE Main 2026A series LCR circuit with R = 20\ Ω , L = 1.6 H and C = 40\ is connected to a variable… JEE Main 2026An a.c. source of angular frequency ω is connected across a resistor R and a capacitor C… JEE Main 2026An inductor of 10 mH, capacitor of 0.1\ μ F and a resistor of 100\ Ω are connected in… JEE Main 2026The figure given below shows an LCR series circuit with two switches S_1 and S_2 . When… JEE Main 2026An inductor stores 16 J of magnetic field energy and dissipates 32 W of thermal energy… JEE Main 2026The electric current in the circuit is given as i=i_ o (t / T) . The r.m.s current for… JEE Main 2026 Full Alternating Current list All JEE Main PYQs