An ac circuit has a 20 $\mu$F capacitor,an 80 mH inductor,and a 60 $\Omega$ resistor in series.If the voltage source has an angular frequency of 1000 rad/s,what is the phase constant for the circuit?
A) 27$^{\circ}$
B) 53$^{\circ}$
C) 45$^{\circ}$
D) 63$^{\circ}$
E) 88$^{\circ}$

Question

Quizplus · Accepted Answer

The phase constant is given by:$$\phi = \arctan\left(\frac{X_L - X_C}{R}ight)$$where:* $X_L$ is the inductive reactance* $X_C$ is the capacitive reactance* $R$ is the resistanceIn this case:* $X_L = 2\pi f L = 2\pi (1000 	ext{ rad/s})(80 	ext{ mH}) = 502.65 \Omega$* $X_C = \frac{1}{2\pi f C} = \frac{1}{2\pi (1000 	ext{ rad/s})(20 \mu	ext{F})} = 79.58 \Omega$Therefore:$$\phi = \arctan\left(\frac{502.65 \Omega - 79.58 \Omega}{60 \Omega}ight) = 26.57^\circ$$which is closest to choice A.

An Ac Circuit Has a 20 μ\muμ F Capacitor,an 80 MH Inductor,and a 60

An Ac Circuit Has a 20 $\mu$ F Capacitor,an 80 MH Inductor,and a 60