The voltage across an AC source and a resistance in series

[Asmaa Mohammad]

Homework Statement

In the circuit below, the RMS of the AC source is 100V, the inductive reactance is 50 ohm, the capacitive reactance is 200 ohm, the resistance is 40 ohm and the current flows in the circuit is 0.644 A. Determine the reading of the voltmeter.

Homework Equations

The Attempt at a Solution

That's my attempt

The voltage value -96.6V was the correct answer according to my textbook, but I determined the voltage across the branch of the capacitor and the inductor, but now I want to determine the voltage across the branch of the AC source and the ohmic resistance, and I think that must give me the same result as the two branches are connected to the same two points.
So, give me some hints how could I determine the voltage acros the branch of the AC source and the resistance branch, and I will work by myself, because I don't know how to do this.

 

[cnh1995]

So, give me some hints how could I determine the voltage acros the branch of the AC source and the resistance branch,

You have all the required data.
Just remember Mr. Kirchhoff..

 

[Asmaa Mohammad]

You have all the required data.
Just remember Mr. Kirchhoff..

But the voltage of the AC source and that of the resistances don't have the same phase, right?
Let's say that we will apply Kirchhoff's voltage law, how would be this, would it be like:
V = Veff - Vr = 100-40 = 60V
It doesn't give the same result.

 

[cnh1995]

But the voltage of the AC source and that of the resistances don't have the same phase, right?

Right. You'll need the complex form of the current ( which maybe you haven't studied yet). It could be a good exercise though, once you study complex numbers.

 

[Asmaa Mohammad]

( which maybe you haven't studied yet).

Yes, I haven't!
Ok, I will put it on my list of problems to solve after studying complex numbers!