Simplified Formulas for Parallel Circuit Resistance Calculations

In this article, we will discuss the formula of resistance in parallel connection. The resistances are connected in the series and parallel combinations to get the desired equivalent or total circuit resistance.

Norton’s Theorem with solved prob...
Norton’s Theorem with solved problem

Formula for Parallel Circuit Resistance Calculations of the same Value Resistances

The equivalent resistance of the equal resistances connected in the parallel combination can be found by dividing the value of one resistance by the number of resistors.

The mathematical expression is;

Simplified Formulas for Parallel Circuit Resistance Calculations

Suppose four resistances of equal value(R) are connected in the parallel combination, the total resistance of the circuit is;

formula for resistance in parallel

Example:

If 100 resistances, each resistance has a 400 Ohms value, are connected in the parallel combinations. What is the total resistance of the parallel circuit?

solved example on parallel resistance circuit

Formula for Parallel Circuit Resistance Calculations of the unequal Value Resistances

The total resistance of two resistances that have unequal resistance can be calculated in the following way.

formula for two resistance in parallel

Example:

The resistance value of the two resistances is 8Ω and 24Ω. These are connected in parallel. Calculate the total resistance of the circuit.

Finding Value of Unknown Resistance when two resistance connected in the parallel Circuit

We can find the value of unknown resistance when it is connected in parallel with a known value resistance.

  • The value of total resistance is given
  • The value of one resistance is known
formula derivation to find  unknown resistance in a parallel resistance circuit

Example:

Find the value of resistance to be added with 24Ω resistance to get a total resistance value of 16Ω when both the resistances are connected in the parallel.

solved example for finding unknown resistance in parallel circuit
solved problem
Note: The total or equivalent resistance of the parallel circuit is always less than the value of the resistance that has minimum resistance among all the resistances. If four resistances have resistance values 5,8,12,20 ohms and are connected in the parallel combination, then the total resistance of the circuit is always less than 5 ohms.
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