How To Calculate Voltage In Parallel Circuit: Example Problems And Detailed Facts


In this article, we shall discuss different methods on How To Calculate Voltage In Parallel Circuits. A parallel connection divides the circuit into branches to let current distributively flow through all of them.

Parallel circuits follow the law of conservation of energy. Voltage can be said as electrical work done per unit charge. Electric fields are conservative, which means electrical work depends only on starting and end points. All the branches have a common initial and final node in a parallel connection. Therefore voltage is equal.

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How To Calculate Voltage In Parallel Circuit- Numerical Examples

How To Calculate Voltage In Parallel Circuit - a parallel RLC circuit
A parallel RLC circuit; “File:Example9d.png” by 1sfoerster is licensed under CC BY-SA 3.0

Q1. As shown in the circuit, two equally valued resistors are joined with a voltage source in parallel. Some values are given: i1= 3 A, equivalent resistance Req= 15 ohm . Find the source voltage Vs

Let us assume R1 = R2 = R ohm. Therefore, the equivalent resistance [Latex] R_{eq} = ( \frac{1} {R} + \frac{1} {R})^{-1} = \frac{R} {2} \Omega [/Latex]. Given R/2 = 15, So the value of each resistor = 15 × 2 = 30 ohm. The value of current i1 is given as 3 A.

As it is a parallel circuit, voltage across a branch will be the same voltage across any other branch, and that will be the supply voltage as well. Hence, the source voltage [Latex] V_{s} = current\; in\; a\; branch \times corresponding\; resistance \; value = i_{1} \times R = 3 \times 30 = 90\; V [/Latex]. 

Q2. A parallel network consists of five resistors, R, 2R, 4R, 8R, and 16R. Net current in the network is I. Find the voltage in the branch containing the 4R resistor.

We shall first find out the equivalent resistance of the network for calculating the voltage at any point of the network. The equivalent resistance in a parallel circuit is [Latex] R_{eq} = ( \frac{1} {R_{1}} + \frac{1} {R_{2}} + \frac{1} {R_{3}}…..+ \frac{1} {R_{n}})^{-1} [/Latex].

Here, [Latex] R_{eq} = ( \frac{1} {R} + \frac{1} {2R} + \frac{1} {4R} + \frac{1} {8R} + \frac{1} {16R})^{-1} = \frac{16R} {31} \: \Omega [/Latex]

The total current in the circuit is given as I Amp.

Therefore, source voltage [Latex] V_{s} = I \times \frac{16R} {31} = \frac{16IR} {31}\; V [/Latex]

We know that a parallel circuit’s source voltage is the same as the voltage in any branch of the circuit. So, the voltage in the branch containing the 4R resistor is 16IR/31 V.

How To Calculate Voltage In Parallel Circuit- FAQs

How to find total voltage in a parallel circuit?

In a parallel circuit, the total voltage is the same as the branch voltages. In other words, the voltage remains the same across all the branches joined in parallel. Branches are just different paths for current.

Steps for calculating voltage in a parallel circuit with resistance and total current given are:

  • Find the equivalent resistance using the formula- [Latex] R_{eq} = ( \frac{1} {R_{1}} + \frac{1} {R_{2}} + \frac{1} {R_{3}}…..+ \frac{1} {R_{n}})^{-1} [/Latex].
  • Multiply Req with the total current.

If only one resistance and the respective current value are given, multiply them to get the voltage.

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How to find missing voltage in a parallel circuit?

By “missing voltage” in a parallel circuit, we mean the supplied voltage as it is the same for all the branches. So, if we have any current and resistance value, we can find out the voltage in the parallel circuit.

Let us understand this with the help of an example. Suppose there are two resistors of 2 ohms and 4 ohms connected in parallel. Current passing through the 2-ohm resistor is given as 1.5 A. We know supply voltage Vs= branch voltage V1 = branch voltage V2. Therefore, missing voltage [Latex] V = iR = 2 \times 1.5 = 3 \times V [/Latex].

How to find source voltage in a series parallel circuit?

According to the principle of a parallel circuit, the voltage in every branch is the same and equal to the source voltage. If the source voltage is Vs and the branch voltages are V1, V2,….Vn then Vs = V1 = V2 =….= Vn.

If the source voltage is given, we already have the branch voltages. If the source voltage is unknown and current values are given, we can find out the voltage with the help of ohm’s law. For example, if the current through a branch is 5 A and the resistance value is 2 ohms, the voltage is simply 5 × 2 = 10 V.

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How to find applied voltage in a parallel circuit?

Applied voltage in parallel circuitry refers to the source voltage or the battery voltage. It is given, or we can compute it with the help of other information provided, such as current and resistance values.

Applied voltages mean the voltage given to an element. In a parallel circuit, the applied voltage is the total voltage. It is also the same as voltage drops in individual branches of the circuit. But if the parallel circuit is not the only part of the network, the applied voltage and branch voltages won’t be equal.

Kaushikee Banerjee

I am an electronics enthusiast and currently devoted towards the field of Electronics and Communications . My interest lies in exploring the cutting edge technologies. I'm an enthusiastic learner and I tinker around with open-source electronics. LinkedIn ID- https://www.linkedin.com/in/kaushikee-banerjee-538321175

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