In a certain series resonant circuit V_C = 125 V, V_L = 125 V and V_R = 40 V. The source voltage is

A series RLC circuit connected to a voltage source is as shown:

For a series RLC circuit, the net impedance is given by:

Z = R + j (XL - XC)   --(1)

XL = Inductive Reactance given by:

XL = ωL

XC = Capacitive Reactance given by:

XL = 1/ωC

Multiplying Equation (1) with current I, we get:

\(I Z = IR + j(IX_L - IX_C)\)

In terms of voltage, the above equation can be written as:

\(V_S = V_R + j(V_L- V_C)\)    ---(2)

At resonance, the inductive reactance becomes equal to the capacitive reactance, i.e.

X_L = X_C

∴ V_L = V_C

Equation (2) can now be written as:

V_S = V_R

∴ At resonance, the net voltage across the source equals the voltage across the resistor. 

Calculation:

Given:

VC = 125 V, VL = 125 V and VR = 40 V

At resonance, the source voltage will be equal to the voltage across the resistor, i.e.

V_S = V_R = 40 V