3. A resistor R is connected to an ac generator. The rms of the emf is E and the

ID: 2121555 • Letter: 3

Question

3. A resistor R is connected to an ac generator. The rms of the emf is E and the driven

angular frequency is wd. The average rate at which energy is dissipated in the resistor is

a. Find an expression for P in terms of R and E.

b. A capacitor is connected in series to the resistor. The average rate at which energy

is dissipated in the resistor is P/2.

i. Determine the power factor. You should get a numeric answer.

ii. Determine the capacitance C. Put your answer in terms of R and wd.

c. The capacitor is removed and replaced with an inductor. When the inductor is

connected in series with the resistor, the average rate at which energy is dissipated

is P/4.

i. Determine the power factor of this circuit. You should get a numeric

answer.

ii. Determine the inductance L. Put your answer in terms of R and wd.

d. The capacitor and inductor from the previous steps are both connected in series to

the resistor.

i. Determine the impedance Z. Put your answer in terms of R.

ii. Determine the power factor. You should get a numeric answer.

iii. Determine the average rate at which energy is dissipated in the resistor.

Put your answer in terms of P.

. P=V2/R

Because E means energy we take V for voltage.

v=-E

so v^2=E^2

P=E^2/R

p=VI coso

cos0=P/VI here P/2

cos0=P/2VI

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