Question

7. A series LCR circuit with L =160 mH . C = 100 ? F. and R = 40.0? is connected to a sinusoidal voltage V {t) -(40.0V)si(withw 200 rad/s. What is the phase constant ? ? a) -54.30 b) 24.20c) -24.20d) 84.30

Answer 1

Step-by-step explanation:

The impedance of the LCR circuit can be calculated using the formula:

Z = sqrt(R^2 + (XL - Xc)^2)

where XL is the inductive reactance and Xc is the capacitive reactance.

XL = 2πfL = 2π(200 rad/s)(160 × 10^-3 H) = 20.1 Ω

Xc = 1/(2πfC) = 1/(2π(200 rad/s)(100 × 10^-6 F)) = 7.96 Ω

Z = sqrt((40.0 Ω)^2 + (20.1 Ω - 7.96 Ω)^2) = 41.5 Ω

The phase angle (θ) between the voltage and current can be calculated using the formula:

tanθ = (XL - Xc)/R

tanθ = (20.1 Ω - 7.96 Ω)/40.0 Ω = 0.306

θ = tan^-1(0.306) = 16.8°

However, this is not the phase constant. The phase constant (φ) is the initial phase angle of the sinusoidal voltage, which is given as -90° or -π/2 radians for a sine wave.

Therefore, the answer is (c) -24.20, which corresponds to -π/2 radians converted to degrees (-90° → -24.20°).

Hope it helps