Given Vs = 43 voltsR = 34 ohmsL = 4.9 mHC = 2.5 microfaradsand frequency  F = 1000HzCalculate the magnitude of the phasor current  I.

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

1 millihenry = 1e-3 henries So, L = 4.9 millihenries = 4.9 * 1e-3 = 0.0049 henries

1 microfarad = 1e-6 farads So, C = 2.5 microfarads = 2.5 * 1e-6 = 0.0000025 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 = 0.0049 henries C = capacitance = 0.0000025 farads

Substituting the values, we get:

Xl = 2 * 3.14159 * 1000 * 0.0049 = 30.79 ohms (approx) Xc = 1 / (2 * 3.14159 * 1000 * 0.0000025) = 63.66 ohms (approx)

Step 3: Calculate the total impedance (Z) of the circuit. The impedance is the square root of the sum of the squares of the resistance (R) and the difference between the reactances (Xl and Xc).

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

Substituting the values, we get:

Z = sqrt(34^2 + (30.79 - 63.66)^2) = 48.02 ohms (approx)

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

I = Vs / Z

where: Vs = phasor voltage = 43 volts Z = impedance = 48.02 ohms

Substituting the values, we get:

I = 43 / 48.02 = 0.895 amps (approx)

So, the magnitude of the phasor current is approximately 0.895 amps.