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

JEE Main · 2022 · 25 Jun 2022 · Shift 2 · Alternating Current

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 F

and

R = 100Ω

. The phase difference

(Φ)

between the applied voltage and resultant current will be :

Answer: (A)

Angular frequency

ω = 3000 rad/s

. Inductive reactance:

X_{L} = ω L = 3000 \times 10 \times 1 0^{- 3} = 30 Ω

. Capacitive reactance:

X_{C} = \frac{1}{ω C} = \frac{1}{3000 \times 25 \times 1 0 ^{- 6}} = \frac{40}{3} Ω

. Net reactance:

X = X_{L} - X_{C} = 30 - \frac{40}{3} = \frac{50}{3} Ω

. Phase difference:

tan ϕ = \frac{X}{R} = \frac{50/3}{100} = \frac{1}{6} \approx 0.167

. Therefore

ϕ = tan^{- 1} (0.17)

JEE Main · 2022 · 25 Jun 2022 · Shift 2 · Single correct option