# The voltage across an AC source and a resistance in series

In summary, the problem involves determining the reading of the voltmeter in a circuit with an AC source, inductive and capacitive reactances, and resistance. By applying Kirchhoff's voltage law, the voltage across the branch of the AC source and resistance branch can be determined. However, since the voltage of the AC source and resistances do not have the same phase, the complex form of current is needed, which may require knowledge of complex numbers.

## 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.

## 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.

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..

cnh1995 said:
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.

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.

cnh1995 said:
( 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!

## 1. What is the relationship between voltage and resistance in a series circuit?

In a series circuit, the voltage across an AC source and a resistance are directly proportional. This means that as the voltage increases, the resistance also increases, and vice versa.

## 2. How does the voltage across an AC source and a resistance in series affect the current in the circuit?

According to Ohm's law, the current in a series circuit is inversely proportional to the total resistance. This means that as the voltage across the AC source and resistance increases, the current in the circuit decreases, and vice versa.

## 3. Can the voltage across an AC source and a resistance in series ever be greater than the voltage of the source?

No, the voltage across any component in a series circuit can never be greater than the source voltage. This is because the total resistance of the circuit limits the flow of current, which in turn determines the voltage across each component.

## 4. How does the frequency of the AC source affect the voltage across the circuit?

The frequency of the AC source does not directly affect the voltage across the circuit, as long as the resistance remains constant. However, a higher frequency may cause changes in the reactance of components in the circuit, which can affect the overall voltage.

## 5. What happens to the voltage across the resistance if another resistance is added in series?

If another resistance is added in series, the total resistance of the circuit increases, which in turn causes a decrease in the voltage across each resistance. This is because the voltage drop is shared between the multiple resistances in the circuit.

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