Given Vs = 78 volts at zero phaseR = 78 ohmsL = 3.8 mHC = 3.3 microfaradsFrequency, F=1000HzCalculate the magnitude of the phasor voltage,  VL in volts.

Given Vs = 78 volts at zero phase

R = 78 ohms

L = 3.8 mH

C = 3.3 microfarads

Frequency, F=1000Hz

Calculate the magnitude of the phasor voltage, VL in volts.

The voltage across the inductor (VL) can be calculated using the formula:

VL = I * Xl

where I is the current through the circuit and Xl is the inductive reactance.

The inductive reactance (Xl) is given by:

Xl = 2πFL

The current (I) can be calculated using Ohm's Law:

I = Vs / Z

where Z is the impedance of the circuit.

The impedance (Z) of a series RLC circuit is given by:

Z = √(R^2 + (Xl - Xc)^2)

where Xc is the capacitive reactance, given by:

Xc = 1 / (2πFC)

Let's calculate the inductive reactance:

Xl = 2π * 1000 * 3.8 * 10^-3 = 7.54 ohms

Now, let's calculate the capacitive reactance:

Xc = 1 / (2π * 1000 * 3.3 * 10^-6) = 48.16 ohms

Now, let's calculate the impedance:

Z = √(78^2 + (7.54 - 48.16)^2) = √(6084 + 1650.4) = √7734.4 = 87.93 ohms

Now, let's calculate the current:

I = Vs / Z = 78 / 87.93 = 0.887 amps

Finally, let's calculate the voltage across the inductor:

VL = I * Xl = 0.887 * 7.54 = 6.68 volts

Therefore, the magnitude of the phasor voltage (VL) is approximately 6.68 volts.