Question

a resistor R is connected in parallel with a 10-ohm inductive reactance. the combination is then connected in series with a 4ohm capacitive reactance. the whole combination is connected across a100 volt, 60hz supply. how much is R if the angle b/h the supply voltage and total current is 45degrees?

Answer 1

The math is a bit difficlt to do here, but here are the steps.
a. find the admitance of the jparallel branch: 1/R + 1/Xl
b. take the reciprocal of that (remember Xl is imag number)
c. add the Xc in series to b result.
Now, for 45 deg, R must equal the magnitude of the imaginary (reactance).