Question

Use phasor techniques to determine the current supplied by the source given that V=8 <0o v, R=4 Ω, C=15 μF, L=4 mH and ω=2000 rad/sec. The current supplied by the source is I = ____ ∠ ____° A. (Round the magnitude to three decimal places and the angle to two decimal places.)

Answer 1

To determine the current supplied by the source in a RLC circuit, we can use phasor techniques. By converting the values of voltage and resistance to phasor form, calculating the reactance of the capacitor and inductor, finding the impedance, and using Ohm's Law, we can determine the current supplied by the source in the given circuit.

Step-by-step explanation:

To determine the current supplied by the source, we can use phasor techniques.

First, let's convert the values of voltage and resistance to phasor form:

For voltage (V): V = 8<0° V

For resistance (R): R = 4 Ω

Next, we can find the impedance (Z) of the circuit using the formula Z = sqrt(R^2 + (X_C - X_L)^2), where X_C is the reactance of the capacitor and X_L is the reactance of the inductor. The reactance of the capacitor is given by X_C = 1/(Cω) and the reactance of the inductor is given by X_L = Lω:

X_C = 1/(15x10^-6 x 2000) = 333.33 Ω

X_L = 4x10^-3 x 2000 = 8 Ω

Now, we can find the impedance:

Z = sqrt((4 Ω)^2 + (333.33 Ω - 8 Ω)^2) = 333.16 Ω

Finally, we can calculate the current using Ohm's Law, where I = V/Z:

I = 8<0° V / 333.16 Ω = 0.024 < -0.18° A

Therefore, the current supplied by the source is I = 0.024 ∠ -0.18° A.