ΜF in a series RLC circuit. The circuit is powered by a 120 V, 60 Hz AC source. The SCR has a firing angle of 45°. Find the current and voltage across the circuit.

To solve this problem, we can use the phasor diagram method. First, we need to find the impedance of the circuit:

Z = R + j(XL - XC)
XL = ωL = 2πfL = 377 × 0.005 = 1.885 Ω
XC = 1/ωC = 1/(377 × 0.00002) = 212.77 Ω
Z = 500 + j(1.885 - 212.77) = 500 - j210.885 Ω

Next, we need to find the current through the circuit. Since the SCR has a firing angle of 45°, it will conduct current for only part of the cycle. We can use the following equation to find the current:

I = Vm/|Z| * sin(ωt + θ)
Vm = 120 V (peak voltage)
θ = 45° (firing angle)

At t = 0, the SCR is not conducting, so the current is zero. At t = π/2ω, the SCR fires and the current starts to flow. We can calculate the current at this point:

I = 120/|Z| * sin(ωt + θ) = 120/|500 - j210.885| * sin(ωt + 45°) = 0.329 A

The current will continue to flow until the end of the cycle, at t = 2π/ω. We can calculate the current at this point:

I = 120/|Z| * sin(ωt + θ) = 120/|500 - j210.885| * sin(ωt + 45°) = -0.329 A

The negative sign indicates that the current is flowing in the opposite direction. We can plot the current waveform as follows:

/\
/ \
____/ \____
π/2 2π/ω


The voltage across the circuit can be found using the following equation:

V = Vm * sin(ωt)

At t = 0, the voltage is zero. At t = π/2ω, the voltage is:

V = 120 * sin(ωt) = 120 * sin(45°) = 84.85 V

The voltage will continue to increase until it reaches its peak value at t = π/ω. We can calculate the peak voltage as follows:

Vp = Vm = 120 V

The voltage will then decrease until it reaches zero at t = π. We can plot the voltage waveform as follows:

/\
/ \
____/ \____
π/2 π


Finally, we can calculate the power dissipated in the circuit:

P = I^2R = (0.329)^2 * 500 = 54.34 W

This power is dissipated in the resistor, since the inductor and capacitor store and release energy without dissipating it.