Resistors in Parallel Formula

When we use resistors in electronic circuits, they can be used in different configurations. We can calculate the resistance for the circuit, or some portion of the circuit, by determining the way of organizing the resistors. Registers are normally organized in series or in parallel. We will describe the concept and resistors in parallel formula with examples. We often call the total resistance of a circuit as the equivalent resistance. Let us learn the concept in an easy way!

                                                                                                                                        Source: en.wikipedia.org

Resistors in Parallel Formula

Concept of Resistors in Parallel

Resistors are often connected in series or in parallel for creating more complex networks. The voltage across resistors in parallel will be the same for each resistor. But, the current will be in proportion to the resistance of each individual resistor.

The purpose of finding the equivalence resistance is that we can replace any number of resistors connected in a parallel combination by the equivalent resistance of the parallel combination resistors.

If two or more resistors are connected in parallel, then the potential difference across all the resistors is the same. Resistors in parallel connection are connected to the same nodes from both ends.

This can be identified by the presence of more than one way for the current to flow. The potential difference across the resistors is the same as that across the resistor which is equal to the supply potential.

The Formula for Parallel Resistors

In electric circuits, we may replace a group of resistors with a single, equivalent resistor. We can find the equivalent resistance of a number of resistors in parallel using the reciprocal of resistance i.e. \(\frac{1}{R}\). The reciprocal of the equivalent resistance is equal to the sum of the reciprocals of each resistance. The unit of resistance is the Ohm, which is equal to a Volt per Ampere. Larger resistors with kilo-Ohm or mega-Ohm resistances are common, as well.

\(\frac{1}{R_{eq}} =\frac{1}{R_1} + \frac{1}{R_2}+ …….\frac{1}{R_n}+…….\)

Where,

\(R_{eq}\)	Equivalent resistance.
\(R_1\)	The resistance of the first resistor.
\(R_2\)	The resistance of the second resistor
\(R_n\)	The resistance of an nth resistor

Major Features of Resistors in Parallel

1. We find Parallel resistance from, and it is smaller than any individual resistance in the combination.
2. Each resistor in parallel has the same voltage of the source applied to it.
3. Parallel resistors do not each get the full current and they divide it.

Solved Examples

Q.1: What is the equivalent resistance of a 1000 kilo-ohm and a 250 kilo-ohm resistor connected in parallel?

Solution: The resistances are both expressed in kilo-Ohms. Thus, there is no need to change the units. We can find the equivalent resistance in kilo-ohm using the formula:

\(\frac{1}{R_{eq}} =\frac{1}{R_1} + \frac{1}{R_2}\)

\(\frac{1}{R_{eq}} =\frac{1}{1000} + \frac{1}{250}\)

= \(\frac {5}{1000} \)

\(R_{eq} = 200\; kilo- \Omega\)

Therefore, the equivalent resistance of the \(1000 kilo- \Omega and 250.0 kilo- \Omega resistors in parallel is 200.0 kilo- \Omega\).

Q.2: What is the equivalent resistance of a 10 ohm, 20 ohm and 30-ohm resistors connected in parallel?

Solution:

Given:

\(R_1\) = 10 ohm

\(R_2\) = 20 ohm

\(R_3\) = 30 ohm

We can find the equivalent resistance in kilo-ohm using the formula:

\(\frac{1}{R_{eq}} =\frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}\)

\(\frac{1}{R_{eq}} =\frac{1}{10} + \frac{1}{20} + \frac{1}{30} \)

= \(\frac{11}{60} \)

\(R_{eq} = \frac{60}{11} \)

\(R_{eq} = 5.55 ohm.\)

Therefore, the equivalent resistance will be 5.55 ohm.