Resistance in Parallel Circuits

Total resistance in a parallel circuit can be found by applying Ohm’s Law. Divide the voltage across the parallel resistance by the total line current as shown in below equation.

Resistance in Parallel Circuit

Example:

Find the total resistance of the circuit shown in Figure 25 if the line voltage is 120 V and total current is 26A.

Solution :

RT = V/IT

RT = 120 / 26 = 4.62 Ω

The total load connected to a 120 V source is the same as the single “equivalent resistance” of 4.62Ω connected across the source (Figure 26). Equivalent resistance is the total resistance a combination of loads present to a circuit.

Equivalent Resistance in a Parallel Circuit

Figure 26 Equivalent Resistance in a Parallel Circuit

The total resistance in a parallel circuit can also be found by using the below equation.

Total Resistance in a Parallel Circuit Formula

Example 1:

Find the total resistance of a 4Ω, and 8Ω ,and a 16Ω resistor in parallel (Figure 27).

Total Resistance in a Parallel Circuit

Figure 27 Total Resistance in a Parallel Circuit

Solution :

Total Resistance in a Parallel Circuit Formula

1 / RT = 1/4 + 1/8 + 1/16

RT = 16/7 = 2.29 Ω

Note: Whenever resistors are in parallel, the total resistance is always smaller than any single branch.

Example 2:

Now add a fourth resistance of 4Ω in parallel to the circuit in Figure 27. What is the new total resistance of the circuit?

Solution:

Total Resistance in a Parallel Circuit Formula

1 / RT = 1/4 + 1/8 + 1/16 + 1/4

RT = 16/11 = 1.45 Ω

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