In a series LRC circuit the rms voltage across the resistor is 80 V,across the capacitor is 120 V,and across the inductor is 60 V.What is the phase constant for this circuit?
A) 27$^{\circ}$
B) -27$^{\circ}$
C) 37$^{\circ}$
D) -37$^{\circ}$
E) -41$^{\circ}$

Question

Quizplus · Accepted Answer

We can use the trigonometric relationships between voltage and current in each component of the circuit to calculate the phase constant. Let θ be the phase constant. Then:

cosθ = VR / V
cos(θ + 2π/3) = VC / V
cos(θ - 2π/3) = VL / V

where VR, VC, and VL are the rms voltages across the resistor, capacitor, and inductor, respectively, and V is the rms voltage across the whole circuit.

Substituting the given values, we get:

cosθ = 0.4
cos(θ + 2π/3) = 0.6
cos(θ - 2π/3) = 0.3

Solving these equations, we find:

θ ≈ -37.2°

Therefore, the answer is D (-37°).

In a Series LRC Circuit the Rms Voltage Across the Resistor