# What Is Voltage Drop In Parallel Circuit:How to Find, Example Problems and Detailed Facts

This article will discuss different methods that can be used to find what is voltage drop In parallel circuit.

By using different methods, we can find voltage drop in a parallel circuit such as:

## Kirchhoff’s Voltage Law (KVL)

German physicist Gustav Kirchhoff introduced Kirchhoff’s voltage law in 1845 for a more accessible analysis of circuit voltage.

According to Kirchhoff’s Voltage Law, the overall algebraic sum of voltage drop or potential difference in a closed path towards a specific single direction equals zero. This law is based on the law of conservation of energy.

Steps to get a potential drop using Kirchhoff’s Voltage law:

• Assume a specific current direction in a closed-loop or mesh. The direction of current can be taken clockwise or anticlockwise.
• Now, while moving in the current direction, define the voltage drop across each element while considering the sign convention of each element in a closed loop or mesh.
• By considering voltage drops across each element, write Kirchhoff’s Voltage law equation by adding all the voltage drops across each element in the loop with the correct electrical sign convention.

## Kirchhoff’s Current Law (KCL)

Kirchhoff’s current law can be applied to any electrical circuit. It does not depend on whether the elements are linear, nonlinear, active, passive, time-invariant, time-variant, etc.

Kirchhoff’s current law is founded on the law of conservation of charge; Kirchhoff’s laws can be applied to both AC and DC circuits. According to Kirchhoff’s current law in any electrical network node point, the algebraic sum of currents meeting at that point or node equals zero. Image Credit: Phatency, Kirchhoff’s first law example, CC BY-SA 3.0

Steps to get a potential drop using Kirchhoff’s Current law:

• Level individual branches with an individual current such as $I_1, I_2,….I_n$. in a specific direction clockwise or anticlockwise, assume voltage drop and resistance of each element in the loop and level them as requirements.
• By using known values of parameters of each loop, we can find unknown voltage drops across any node or junction of a parallel circuit combination.
• Apply Ohm’s law to relate the current-voltage and resistance across each element of the loop.
• Finally, solve for unknown values.

Note: During network circuit analysis levelling, all network junctions use different numbers or alphabets. When forming the equation, always consider the direction of current and voltage polarity according to conventional network signs. During calculation, only include those loops needed for an easy and quick solution.

KCL is always applied to a closed boundary.

## Nodal Analysis

Nodal analysis is the application of Ohm’s Law along with Kirchhoff’s Current Law (KCL).

Nodal voltage analysis is the application of Kirchhoff’s current law to find the unknown voltage drop across each node. This method uses a minimum number of equations to determine the unknown nodal voltages and is best suited for parallel circuit combinations.

Node voltage analysis provides us with an easier way to find the voltage at each node of an electrical circuit. With a large number of branches, the Nodal analysis Method can get Complex with an increased number of equations.

In this method, one node of the network is considered a datum or reference or zero potential nodes. The number of equations is n-1 for the ‘n’ number of each independent node.

The procedure of nodal analysis:

• Redraw the circuit diagram by converting all voltage sources into a proportional current source circuit using the source transformation method.
• Level all notes with letters on the number and select a node to take it as a reference for other nodes (which is called a datum or zero potential nodes)
• Write equations by considering the direction of the current flowing into or out of each node with respect to the reference node.
• Solve the equation to get the unknown node voltage or unknown branch current.
• If possible, choose a node as a reference node that is connected to a voltage source.
• Use Ohm’s law to express the relation of resistor current in terms of node voltage.

#### Nodal analysis with a voltage source:

• Supernode formation is a particular type of node which can form.
• A supernode is formed when a voltage source is connected between two non-reference nodes and parallel with any elements.
• A supernode require both KVL and KCL to be applied.
• Supernode does not have its own voltage.

## Current Division

In parallel combination, the voltage across each branch will be identical, but the current through each branch may be different depending upon the overall resistance of the branch.

The current division rule is an application of solving a circuit by Norton’s theorem, as the current in a branch of a parallel circuit is inversely proportional to the overall resistance of the branch.

By using the current division circuit rule, the unknown voltage across any element can be determined.

#### Current division principle:

$V= Z_e. I$

$Z_e$ = overall impedance of a circuit.

$Z_1$ and $Z_2$ is the impedance of branch 1 and 2,

$V = \frac{Z_1Z_2 I}{(Z1 + Z2)}$

Where I is the overall current

$I_1 = \frac{I Z_2}{Z_1 + Z_2}$

$I_2 = \frac{I Z_1}{Z_1 + Z_2}$

By KCL, $I = I_1 + I_2$

#### Example of Current division problem:

In the given figure, there are three resistors connected in parallel combination with each other with a current source Is voltage across $R_1 is V_1$ where the voltage across $R_2 is V_2$ voltage across $R_3$ is $V_3$ . Image Credit: A parallel circuit with three resistors and one source.

$i_1 R_1 = i_2 R_2 = i_3 R_3$

Or $i_1= \frac{V_s}{R_1}, i_2 =\frac{V_s}{R_2}, i_3 =\frac{V_s}{R_3}$

Apply Kirchhoff’s Current Law (KCL) at node:

$I = i_1 + i_2 +i_3$

$I = \frac{V_s}{R_1} +\frac{V_s}{R_2} + \frac{Vs}{R_3} = Vs (\frac{1}{R_1}+ \frac{1}{R_2} +\frac{1}{R_3} ) = \frac{Vs}{Req}$

Where $R_e$ is defined as :

$1/R_e = 1/R\frac{1}{R_1}+ \frac{1}{R_2} +\frac{1}{R_3} = \frac{1}{R_e}}$

For calculating the value of $I_1, I_2$ and $I_3$ , as

$I_1 = \frac{R_2 R_3 i}{(R_1 R_2 + R_2 R_3 + R_3 R_1 )}$

$I_2 = \frac{R_1 R_3 i}{(R_1 R_2 + R_2 R_3 + R_3 R_1 )}$

$I_3 = \frac{R_1 R_2 i}{(R_1 R_2 + R_2 R_3 + R_3 R_1 )}$

By finding $I_1, I_2, or I_3$ , we can get the voltage drop across each resistor as $V_1= i_1R_1, V_2 =i_2R_2 and V_3 = i_3R_3.$

## Superposition Theorem

When a circuit is designed with more than one power source, then Superposition principle can be used.

According to the superposition principle, the voltage across any element in a linear circuit is the algebraic sum of the voltage across the element when only one independent source is applied across if there are two or more independent sources in the circuit.

Steps to use superposition principle in any circuit:

• Disconnect all sources except one source and find the output voltage or current due to only one active source in the circuit.
• Repeat the above statement for each individual source.
• Finally, find the overall summation of the current and voltage across every element well considering the polarity or correct electrical sign convention.

Assume there are ‘n’ number of elements in a closed loop and are connected in series with each other. The voltage drop in each element is levelled as $V_1, V_2, V_3, V_4 …. V_n.$ then

$V_1 + V_2 + V_3 ….. +V_n = 0$

If there is an ‘n’ number of branches connected to a node, then each current is labelled as $I_1 I_2 I_3 … I_n$ let’s assume the current going towards the node is considered positive, and the current leaving from the node is taken as negative then.

$I_1 + I_2 + I_3 + I_4 …. I_n = 0$

# How to find voltage drop in a parallel circuit

The parallel combination of elements can be defined as when the voltage drop or potential difference across each branch connected between two points is identical.

Analysis of parallel circuits: Image Credit: a parallel circuit example with four resistances.
• The voltage drop across every branch in the parallel combination is identical to the voltage source.
• Determine the current through each branch of the circuit by using Ohm’s law.
• Use Kirchhoff’s current law to find out the total current flow through the circuit.
• The nodal analysis method is based on the application of KVL, KCL and Ohm’s law.
• Level all required circuit parameters. Image: Circuit after naming all the nodes with numbers.
• All nodes of the circuit are named as 1, 2, 3, and 4.
• Now select one node as a reference node.
• Now assign the flow of current in every branch of the circuit.
• Assign the voltage of each node. The voltage of node 1 is $V_1$, node 2 is $V_2$, node 3 is $V_3$. Image: Circuit after assuming the direction of the currents.

Apply Kirchhoff’s current law at node 2, then

$i_1 = i_2 + i_3$

now $i_1 = \frac{V_s-V_2}{R_1}$

$i_2 = \frac {V_2}{R_2}$

$i_3 = \frac {V_2- V_3}{ R_3}$

now put the value of $i_1, I_2, I_3,$ as

$\frac{V_s-V_2}{R_1} – \frac {V_2}{R_2} – \frac {V_2- V_3}{ R_3} = 0$

Apply Kirchhoff’s current law at node 3

$\frac{ V_2 – V_3}{ R_3} -\frac {V_3}{R_4} = 0$

Finally solve all equations to get the required potential drop or voltage drop at a point or node.

Sneha Panda

I have graduated in Applied Electronics and Instrumentation Engineering. I'm a curious-minded person. I have an interest and expertise in subjects like Transducer, Industrial Instrumentation, Electronics, etc. I love to learn about scientific researches and inventions, and I believe that my knowledge in this field will contribute to my future endeavors. LinkedIn ID- https://www.linkedin.com/in/sneha-panda-aa2403209/