In a series RLC circuit, R = 1 kΩ, L = 10 μH, C = 1 μF and source voltage = 10 V, the current in the circuit at resonance is   

Concept:

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

Z = R + j (XL - XC)

XL = Inductive Reactance given by:

XL = ωL

XC = Capacitive Reactance given by:

XL = 1/ωC

The magnitude of the impedance is given by:

\(|Z|=\sqrt{R^2+(X_L-X_C)^2}\)

The current flowing across the series RLC circuit will be:

\(I=\frac{V}{|Z|}\)

At resonance, XL = XC, resulting in the net impedance to be minimum. This eventually results in the flow of maximum current of:

\(I=\frac{V}{R}\)

Application:

With R = 1 kΩ and V = 10 V, we get:

\(I=\frac{10}{1k}\)

I = 10 mA