A series circuit contains R = 150 Ω, and C = 10uf, and connected to a 110 volt source. If the source frequency is 120Hz , find the current flowing through R.

The answer seems to says it was 0.55A

SOLUTION:
Xc = 1/(2pifC) = 132.63 Ω
Z = √(150^2 + 132.63^2)
Z = 200.23 Ω

I = V/Z = 110/200.23 = 0.5494A

θ = arctan(- 132.63/150)
θ = -41.48

Rec(0.5494 < -41.48)
0.5494 = 0.4116 - 0.3638998j

where Ir = 0.4116 ===> does not = to the answer key given

 

You found the answer for the current flow in the circuit as 0.5494A. In a series circuit all the currents are the same. You do not need any further calculations to determine the current in R.

 

I think possibly the OP is expecting the in-phase (or real) component of the current to equal the resistor current. This would only be possible with a parallel circuit.