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MHT CET 202623 AprilEvening Shift
Exam
MHT CET
Year
2026
Date
23 April
Shift
Evening Shift
Subject
Physics
Chapter
Alternating Current

MHT CET 2026 · 23 April · Evening Shift · Physics · Alternating Current

If a coil of inductance L and resistance R is connected to AC...

If a coil of inductance L and resistance R is connected to AC source with voltage V and angular frequency ω\omega and current I, then the inductance L is

Options

  1. A1ω2\dfrac{1}{\omega^2}\left(\sqrt{ (VrmsIrms)2−\left(\dfrac{V_{rms}}{I_{rms}}\right)^2- R^2}\right)
  2. B1ω\dfrac{1}{\omega}\left(\sqrt{ (VrmsIrms)2−\left(\dfrac{V_{rms}}{I_{rms}}\right)^2- R^2}\right)
  3. C1ω((VrmsIrms)2−R2)\dfrac{1}{\omega} \left( \left(\dfrac{V_{rms}}{I_{rms}}\right)^ 2-R²\right)
  4. D1ω2\dfrac{1}{\omega^2}\left(\sqrt{ (VrmsIrms)3−\left(\dfrac{V_{rms}}{I_{rms}}\right)^3- R^3}\right)

Correct answer

B. 1ω\dfrac{1}{\omega}\left(\sqrt{ (VrmsIrms)2−\left(\dfrac{V_{rms}}{I_{rms}}\right)^2- R^2}\right)

Step-by-step solution

The impedance ZZ of a coil having inductance LL and resistance RR in an AC circuit is given by Z=R2+XL2Z = \sqrt{R^2 + X_L^2}, where the inductive reactance is XL=ωLX_L = \omega L.

From Ohm's law for AC circuits, the impedance is also given by Z=VrmsIrmsZ = \dfrac{V_{rms}}{I_{rms}}.

Equating the two expressions for impedance:

R2+ω2L2=VrmsIrms\sqrt{R^2 + \omega^2 L^2} = \dfrac{V_{rms}}{I_{rms}}

Squaring both sides:

R2+ω2L2=(VrmsIrms)2R^2 + \omega^2 L^2 = \left(\dfrac{V_{rms}}{I_{rms}}\right)^2

Rearranging to solve for ω2L2\omega^2 L^2:

ω2L2=(VrmsIrms)2−R2\omega^2 L^2 = \left(\dfrac{V_{rms}}{I_{rms}}\right)^2 - R^2

Taking the square root of both sides:

ωL=(VrmsIrms)2−R2\omega L = \sqrt{\left(\dfrac{V_{rms}}{I_{rms}}\right)^2 - R^2}

L=1ω(VrmsIrms)2−R2L = \dfrac{1}{\omega} \sqrt{\left(\dfrac{V_{rms}}{I_{rms}}\right)^2 - R^2}

Answer: \dfrac{1}{\omega} \left(\sqrt{ \left(\dfrac{V_{rms}}{I_{rms}}\right)^2- R^2}\right)
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