Equivalent Resistance Formula

More resistance means for the less current flowing through the circuit. If the electrical circuit is having many resistances connected, then we need to find their accumulated resistance value. Thus, the equivalent resistance is a different way of indicating the total resistance. It will be calculated differently for series and parallel circuits. The equivalent resistance of any such network will be the single resistor which can replace the entire network with the same effect. This topic will explain the equivalent resistance formula with examples. Let us learn it!

What is the Equivalent Resistance?

The equivalent resistance is where the total resistance connected either in parallel or in series. Electrical resistance shows that how much energy will be required when we move the charges i.e. current through the circuit. If we need lots of energy, then the resistance necessary should also be high. The equivalent resistance of a network is the single resistor which can replace the entire network in such a way that for a certain applied voltage as V we will get the same current as I.

Source: en.wikiversity.org

The Formula for Equivalent Resistance

1] Equivalent resistance formula for series resistance:

In electrical circuits, it is possible to replace a group of resistors with a single equivalent resistor. The equivalent resistance of a number of resistors in series will be the sum of the individual resistances. The unit of resistance is the Ohm i.e. in symbol \Omega.

Thus, Equivalent Resistance will be resistor_ 1 + resistor_ 2 + resistor_3 + …..

Mathematically, \(R_{eq} will be (R_1 + R_2 + R_3 + …….)\)

\(R_{eq}\)	The equivalent resistance
\(R_1\)	The resistance of the first resistor
\(R_2\)	The resistance of the second resistor
\(R_3\)	The resistance of the third resistor

 2] Equivalent resistance formula for parallel resistance:

In electrical circuits, it is often possible to replace a group of resistors with a single but equivalent resistor. The equivalent resistance of a number of resistors connected in parallel can be computed using the reciprocal of the resistance i.e.  \frac{1} {R}. The reciprocal of the equivalent resistance will be equal to the sum of the reciprocals of each resistance. The unit of resistance is the Ohm i.e. \Omega.

Thus, \(\frac {1} {equivalence resistance} = \frac {1}{resistor_1} + \frac {1}{resistor_2}+\frac {1}{resistor_3} + …\)

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

Solved Examples for Equivalent Resistance Formula

Q.1: What will be the equivalent resistance of \(480 \Omega,  320 \Omega, and 100 \Omega\) resistors connected in series?

Solution: Given values are,

• \(R_1 = 480 \Omega\)
• \(R_2 = 320 \Omega\)
• \(R_3 = 100 \Omega\)

Now, formula is, \(R_{eq} = R_1 + R_2 + R_3 \\\)

\(= 480 + 320 + 1000 \\\)

\(= 900 \Omega\)

Therefore, the equivalent resistance will be \(900 \Omega.\)

Q.2: What will be the equivalent resistance if \(5 \Omega and 20\Omega\) are connected in parallel?

Solution: Given,

\(R_1 = 5 \Omega\)

\(R_2 = 20 \Omega\)

Now , formula is,

\(\frac {1} { R_{eq}} = \frac {1}{5} + \frac {1}{20}\\\)

\(\frac {1} { R_{eq}} = \frac{1}{4} \\\)

\(R_{eq} = 4 \Omega\)

Equivalent resistance in parallel will be \(4 \Omega.\)