# AC voltage across a parallel branch

• Jahnavi
In summary, the conversation discusses the calculation of the net resistance and current in a circuit with a voltage source and two branches. The impedance triangle is used to determine the net reactance in the upper branch and the voltage across the resistor. The conversation also addresses the use of complex numbers to manipulate reactance values and the importance of considering phase shifts in reactive components. Ultimately, it is concluded that the net resistance of the branches cannot be combined as if they were resistors, but the impedances can be manipulated using complex arithmetic.
Jahnavi

## The Attempt at a Solution

I am assuming that the given value of voltage applied is an RMS value .

Same voltage is applied across both the branches .

In the upper branch the net resistance is the sum of capacitive reactance of the capacitor and resistance of the resistor .

Using Impedance triangle , the net reactance is 100√2 Ohms and the net applied voltage across the branch is ahead of the voltage across the resistor by a phase π/4 . Hence voltage across the resistor is 20/√2 or 10√2 volts i.e option 3) .

This is also the given answer .

But I think option 2) is also correct . The net resistance of the upper branch is 100√2 Ohms and that of the lower branch is 50√2 Ohms .

The resistances in the two branches are in parallel .

The net resistance across the voltage source is (100√2)(50√2)/(100√2 + 50√2) = 10000/(150√2) Ohms

Current in the circuit = 0.3√2 Ohms . This makes option 2) also correct .

Is option 2) also correct along with option 3) ?

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Jahnavi said:
But I think option 2) is also correct . The net resistance of the upper branch is 100√2 Ohms and that of the lower branch is 50√2 Ohms .

The resistances in the two branches are in parallel .

The net resistance across the voltage source is (100√2)(50√2)/(100√2 + 50√2) = 10000/(150√2) Ohms

Current in the circuit = 0.3√2 Ohms . This makes option 2) also correct .

Is option 2) also correct along with option 3) ?
No, you can't combine resistor+reactance magnitudes as though they were resistances. It would be akin to "adding" vectors by their magnitudes alone.

Instead what you can do is use complex numbers to write the resistances and reactances in the form of impedances. Then you can combine these impedance values using the same formulas that you would for resistors.

Jahnavi
gneill said:
No, you can't combine resistor+reactance magnitudes as though they were resistances.

Are you implying that net resistance of the upper branch is 100√2 Ohms and that of lower branch is 50√2 Ohms but the two resistances are not in parallel ?

Jahnavi said:
Are you implying that net resistance of the upper branch is 100√2 Ohms and that of lower branch is 50√2 Ohms but the two resistances are not in parallel ?
While you can say that the "net resistance" of the individual branches are what you've written, you cannot combine those values as if they were resistors. They are not pure resistances, but the magnitudes of the branch impedances.

The inductance and capacitance each present a reactance, not a resistance. Reactance not only "resists" current flow, but also produces a phase shift of the voltage developed across it versus the current flowing through it.

To conveniently work with reactive components we write the reactance as impedance using complex numbers. These impedance values can then be manipulated just as you would resistor values, the only difference being that you need to perform complex arithmetic. The complex math automatically takes care of dealing with the phase shifts that the components create.

Jahnavi
Jahnavi said:
Are you implying that net resistance **impedance of the upper branch is 100√2 Ohms and that of lower branch is 50√2 Ohms but the two resistances are not in parallel ?
The two resistances aren't in parallel, but the two impedances are.
As gneill mentioned, you need to represent the impedances in complex form.

Jahnavi

## What is AC voltage?

AC voltage refers to the fluctuating electrical potential difference between two points in an alternating current (AC) circuit. This means that the voltage changes direction and magnitude over time, as opposed to direct current (DC) which has a constant voltage.

## What does it mean for voltage to be across a parallel branch?

When discussing parallel branches in an electrical circuit, voltage across a parallel branch refers to the potential difference between two points in a parallel branch of the circuit. This means that the voltage is measured across the components in the branch, rather than through them.

## How is AC voltage measured across a parallel branch?

AC voltage across a parallel branch is typically measured using a voltmeter. The voltmeter is connected in parallel to the branch and measures the potential difference between the two points. It is important to note that the voltmeter should have a high impedance to avoid altering the voltage in the circuit.

## What factors affect the AC voltage across a parallel branch?

The AC voltage across a parallel branch is affected by the individual impedance of the components in the branch, as well as the frequency of the AC signal. The voltage will also vary depending on the position of the components within the branch and the overall load on the circuit.

## Why is it important to understand AC voltage across a parallel branch?

Understanding AC voltage across a parallel branch is important for designing and troubleshooting electrical circuits. It allows for the proper selection of components and helps identify any issues that may arise in the circuit. It is also crucial for ensuring the safe and efficient operation of the circuit.

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