For the circuit below a. Determine I , V R , and V C in phasor form. b. Calculat

Question

For the circuit below

a. Determine I, VR, and VC in phasor form.
b. Calculate the total power factor, and indicate whether it is leading or lagging.

c. Calculate the average power delivered to the circuit.

d. Draw the impedance diagram.

e. Draw the phasor diagram of the voltages E, VR, and VC, and the current I.

f. Find the voltages VR and VC using the voltage divider rule, and compare them with the results of part (a).

g. Draw the equivalent series circuit of the above as far as the total impedance and the current i are concerned.

Explanation / Answer

The magnitude of the current is:

I = V/Z = .982A

From this, the magnitude of the impedance "Z" is:

Z = V/I = 115/.982 = 117 ohms

| Z | = sqrt( XL^2 + R^2)

where "XL" is the "reactance" of the inductor.

Z^2 = XL^2 + R^2

R^2 = Z^2 - XL^2

R = sqrt( Z^2 - XL^2 ) = sqrt( 117^2 - (76.4)^2 ) = 88.8 ohms

There is no average power developed in the inductor, only the resistor develops average power.

P = I^2 * R = (.982)^2*88.8 = 85.6W

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