For a particular RLC series circuit, the capacitive reactance is 7.95 Ω , 7.95 Ω, the inductive reactance is 47.7 Ω , 47.7 Ω, and the maximum voltage across the 69.5 Ω 69.5 Ω resistor is 28.5 V . 28.5 V. What is the maximum voltage across the circuit?
Question
Answer:
51.3165 V
Explanation:
The maximum voltage across the circuit is given as,
V’ = IXc + IXl + Vr ……………… Equation 1
Where V’ = The maximum voltage across the circuit, I = current, Xc = capacitive reactance, Xl = inductive reactance, Vr = voltage cross the resistor.
From Ohm’s Law,
V = IR……….. Equation 2
I = V/R……….. Equation 3
Given: V = 28.5 V, R = 69.5 Ω
Substitute into equation 3
I = 28.5/69.5
I = 0.41 A.
Also Given: Xc = 7.95 Ω, Xi = 47.7 Ω, Vr = 28.5 V.
Substitute into equation 1
V’ = 7.95(0.41) + 47.7(0.41) + 28.5
V’ = 3.2595+19.557+28.5
V’ = 51.3165 V