Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 202524 JanuaryMorning Shift
Exam
JEE Main
Year
2025
Date
24 January
Shift
Morning Shift
Subject
Physics
Chapter
Alternating Current

JEE Main 2025 · 24 January · Morning Shift · Physics · Alternating Current

An alternating current is given by I= I _ A ω t+ I _ B ω t . The...

An alternating current is given by I=\mathrm{I}=\mathrm{I}Asin⁡ωt+_{\mathrm{A}} \sin \omega \mathrm{t}+\mathrm{I}Bcos⁡ωt_{\mathrm{B}} \cos \omega \mathrm{t}. The r.m.s current will be

Options

  1. A\frac{\left|\mathrm{I}A+_{\mathrm{A}}+\mathrm{I}_{\mathrm{B}}\right|}{\sqrt{2}}
  2. B\sqrt{\frac{\mathrm{I}A2+_{\mathrm{A}}^2+\mathrm{I}_{\mathrm{B}}^2}{2}}
  3. C\sqrt{\mathrm{I}A2+_{\mathrm{A}}^2+\mathrm{I}_{\mathrm{B}}^2}
  4. D\frac{\sqrt{\mathrm{I}A2+_{\mathrm{A}}^2+\mathrm{I}_{\mathrm{B}}^2}}{2}

Correct answer

B. \sqrt{\frac{\mathrm{I}A2+_{\mathrm{A}}^2+\mathrm{I}_{\mathrm{B}}^2}{2}}

Step-by-step solution

I=IAsin⁡ωt+IBcos⁡ωtIma=IA2+IB2 So, IRMS=IA2+IB22\begin{aligned} & I=I_{\mathrm{A}} \sin \omega t+I_B \cos \omega t \\ & I_{\mathrm{ma}}=\sqrt{I_A^2+I_B^2} \\ & \text{ So, } I_{\mathrm{RMS}}=\sqrt{\frac{I_A^2+I_B^2}{2}}\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