Verified Solution • 2025–26 Session moderate

QJEEM22Ph3b78: JEE Main 2022 Physics - Class 12 JEEM22Ph3b78 Solution: A sinusoidal voltage V(t) = 210 sin 3000 t volt is applied to a …

A sinusoidal voltage V(t) = 210 sin 3000 t volt is applied to a series LCR circuit in which L = 10 mH, C = 25 μ\mu F and R = 100 Ω\Omega . The phase difference ( Φ\Phi ) between the applied voltage and resultant current will be :

Multiple Choice Options

  • A tan −- 1(0.17)
  • B tan −- 1(9.46)
  • C tan −- 1(0.30)
  • D tan −- 1(13.33)

Step-by-Step Verified Solution

XL=3000×10×10−3=30 Ω{X_L} = 3000 \times 10 \times {10^{ - 3}} = 30\,\Omega

XC=13000×25×106=403 Ω{X_C} = {1 \over {3000 \times 25}} \times {10^6} = {{40} \over 3}\,\Omega

So XL−XC=30−403=503 Ω{X_L} - {X_C} = 30 - {{40} \over 3} = {{50} \over 3}\,\Omega

tan⁡θ=XL−XCR=50/3100=16\tan \theta = {{{X_L} - {X_C}} \over R} = {{50/3} \over {100}} = {1 \over 6}

So θ=tan⁡−1(0.17)\theta = {\tan ^{ - 1}}(0.17)

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