An RLC circuit has a voltage source Et30sin50t V a resistor

An RLC circuit has a voltage source E(t)=30sin50t V, a resistor of 120 ohms, an inductor of 4 H, and a capacitor of (2200)^-1 F. Find the steady-state current for this circuit. Find the resonance frequency for the circuit. Assuming the circuit has no charge and no current at t=0, using matlab plot the current and voltage on the same graph. I have to have the graph.

Solution

the impedance of the circuit is R + jXL + j/ XC

Z = sqrt ( R² + (XL - XC)²)

XL = wL = 50 x 4 = 200 XC = 1/wc = 2200/50 = 44 where w = angulr velocity of voltage

Steady state current = V/ sqrt ( R² + (XL - XC)²) = 30 sin 50t / sqrt ( 120² + (200 - 44)²)

= 0.152 sin 50t

resonance frequency = 1/(2 pi sqrt (LC) ) = 3.73 HZ