Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET 202626 AprilMorning Shift
Exam
MHT CET
Year
2026
Date
26 April
Shift
Morning Shift
Subject
Physics
Chapter
Alternating Current

MHT CET 2026 · 26 April · Morning Shift · Physics · Alternating Current

In a series LCR circuit R = X_L = 2X_C . The impedance of the...

In a series LCR circuit R=XL=2XCR = X_L = 2X_C. The impedance of the circuit and phase difference between 'V' and 'I' respectively will be

Options

  1. AR2,tan⁡−1(0.5)\dfrac{R}{2}, \tan^{-1}(0.5)
  2. B52 R,tan⁡−1(0.5)\dfrac{\sqrt{5}}{2}\ R, \tan^{-1}(0.5)
  3. C52 R,tan⁡−1(0.2)\dfrac{\sqrt{5}}{2}\ R, \tan^{-1}(0.2)
  4. DR2,tan⁡−1(0.2)\dfrac{R}{2}, \tan^{-1}(0.2)

Correct answer

B. 52 R,tan⁡−1(0.5)\dfrac{\sqrt{5}}{2}\ R, \tan^{-1}(0.5)

Step-by-step solution

Given R=XL=2XCR = X_L = 2X_C

XL=RX_L = R

XC=R2X_C = \dfrac{R}{2}

The impedance of the series LCR circuit is given by:

Z=R2+(XL−XC)2Z = \sqrt{R^2 + (X_L - X_C)^2}

Substituting the values:

Z=R2+(R−R2)2Z = \sqrt{R^2 + \left(R - \dfrac{R}{2}\right)^2}

Z=R2+(R2)2=R2+R24=52RZ = \sqrt{R^2 + \left(\dfrac{R}{2}\right)^2} = \sqrt{R^2 + \dfrac{R^2}{4}} = \dfrac{\sqrt{5}}{2} R

The phase difference ϕ\phi between voltage and current is given by:

tan⁡ϕ=XL−XCR\tan \phi = \dfrac{X_L - X_C}{R}

tan⁡ϕ=R−R2R=R2R=0.5\tan \phi = \dfrac{R - \dfrac{R}{2}}{R} = \dfrac{\dfrac{R}{2}}{R} = 0.5

ϕ=tan⁡−1(0.5)\phi = \tan^{-1}(0.5)

Answer: 52 R,tan⁡−1(0.5)\dfrac{\sqrt{5}}{2}\ R, \tan^{-1}(0.5)
Practice Alternating Current on Quantrex Academy →

More from Alternating Current

A step down transformer connected to an a.c. mains of 220 V is made to operate at 5.5 V… MHT CET Medical 2026Which phasor diagram represents LCR circuit at resonance? MHT CET Medical 2026For an R-L series circuit, the power factor is 3 2 , for R-L frequency f Hz. If the… MHT CET Medical 2026In an AC circuit, the current is I = 100 (5t) A. The value of I_ rms is MHT CET Medical 2026The ratio of power factor of purely resistive circuit to purely reactive circuit is ( 0^… MHT CET Medical 2026In an LCR series circuit, at resonance, MHT CET Medical 2026In an AC circuit, E and I are given by E = 150 (150t) V and I = 150 (150t + (π)/(3)) A.… MHT CET Medical 2026A series LCR circuit is connected across a source E of e.m.f. E=15 ( 50 π t- (π)/(3)).… MHT CET Medical 2026 Full Alternating Current list All MHT CET Medical PYQs