physics question please help?

Question

An inductor and a resistor are connected in series. When connected to a 60 Hz, 90 V (rms) source, the voltage drop across the resistor is found to be 45 V (rms) and the power delivered to the circuit is 15 W.
(a) Find the resistance.
R = ohm
(b) Find the inductance.
L = H

Answer 1

Power=Watts=VxAmps=15=90 x Amps
So amps=6

and Volts = amps x resistance. so

90=6x R and R=15 total for the entire circuit. R + Inductor

Now this is a series AC circuit so the inductance is in Ohms and its additive in series, so current is same in the circuit regardless.

so again V across the resistor (90-45) = 45 since a 45 drop in volts occurs.

So the voltage across the coil would also be 45 volts drop since the voltage drops must add up to 90 Therefore the inductance of the coil is equal to the resistance of the resistor in ohms. again v=ir and the inductance is 1/2 the total R or 15/2=7.5 ohms.