Question

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

• A. tan^–1(0.17)
• B. tan^–1(9.46)
• C. tan^–1(0.30)
• D. tan^–1(13.33)

Answer 1

The Correct Option is A

The correct option is((A); tan^–1(0.17).

X_L = 3000 × 10 × 10^–3 = 30Ω

\(X_c=\frac{1}{3000x25}×10^6=\frac{40}{3}Ω\)

So

\(X_L-X_C=30-\frac{40}{3}=\frac{50}{3}Ω\)

\(tanθ=\frac{X_L-X_C}{R}=\frac{50/3}{100}=\frac{1}{6}\)

So

\(θ=tan^{-1}(0.17)\)