Given Vs = 79 voltsR = 13 ohmsL = 2.1 mHC = 1.3 microfaradsFrequency, F= 1000HzCalculate the magnitude of the phasor voltage, Vc, in volts.

Step 1: Convert the inductance from millihenries to henries and the capacitance from microfarads to farads.

1 millihenry = 1e-3 henries So, L = 2.1 millihenries = 2.1 * 1e-3 = 0.0021 henries

1 microfarad = 1e-6 farads So, C = 1.3 microfarads = 1.3 * 1e-6 = 0.0000013 farads

Step 2: Calculate the reactance (Xl) of the inductor and the reactance (Xc) of the capacitor using the formulas:

Xl = 2 * π * F * L Xc = 1 / (2 * π * F * C)

where: π = 3.14159 (approx) F = frequency = 1000 Hz L = inductance = 0.0021 henries C = capacitance = 0.0000013 farads

Substituting the values, we get:

Xl = 2 * 3.14159 * 1000 * 0.0021 = 13.19 ohms (approx) Xc = 1 / (2 * 3.14159 * 1000 * 0.0000013) = 122.52 ohms (approx)

Step 3: Calculate the magnitude of the phasor current (I) using Ohm's law:

I = Vs / sqrt(R^2 + (Xl - Xc)^2)

where: Vs = phasor voltage = 79 volts R = resistance = 13 ohms Xl = inductive reactance = 13.19 ohms Xc = capacitive reactance = 122.52 ohms

Substituting the values, we get:

I = 79 / sqrt(13^2 + (13.19 - 122.52)^2) = 0.64 amps (approx)

Step 4: Calculate the magnitude of the phasor voltage across the capacitor (Vc) using Ohm's law:

Vc = I * Xc

where: I = phasor current = 0.64 amps Xc = capacitive reactance = 122.52 ohms

Substituting the values, we get:

Vc = 0.64 * 122.52 = 78.41 volts (approx)

So, the magnitude of the phasor voltage across the capacitor is approximately 78.41 volts.