Given phasor voltage Vs = 30 volts (@ zero phase)R = 16 ohmsC = 910 microfaradsFrequency, F = 100 HzCalculate the magnitude of the phasor current I in amps

Step 1: Convert the capacitance from microfarads to farads.

1 microfarad = 1e-6 farads So, C = 910 microfarads = 910 * 1e-6 = 0.00091 farads

Step 2: Calculate the reactance (Xc) of the capacitor using the formula:

Xc = 1 / (2 * π * F * C)

where: π = 3.14159 (approx) F = frequency = 100 Hz C = capacitance = 0.00091 farads

Substituting the values, we get:

Xc = 1 / (2 * 3.14159 * 100 * 0.00091) = 1.75 ohms (approx)

Step 3: Calculate the total impedance (Z) of the circuit. Since the resistor and capacitor are in series, the impedance is the square root of the sum of the squares of the resistance (R) and reactance (Xc).

Z = sqrt(R^2 + Xc^2)

Substituting the values, we get:

Z = sqrt(16^2 + 1.75^2) = 16.15 ohms (approx)

Step 4: Calculate the magnitude of the phasor current (I) using Ohm's law:

I = Vs / Z

where: Vs = phasor voltage = 30 volts Z = impedance = 16.15 ohms

Substituting the values, we get:

I = 30 / 16.15 = 1.86 amps (approx)

So, the magnitude of the phasor current is approximately 1.86 amps.