How To Calculate Total Resistance In A Series Parallel Combination Circuit

How to Calculate Total Resistance in a Series-Parallel Combination Circuit

A series-parallel combination circuit is a circuit that contains both series and parallel connections of resistors. To calculate the total resistance of a series-parallel combination circuit, you can use the following steps: 1.

Identify the series resistors.

Series resistors are resistors that are connected end-to-end, such that the same current flows through each resistor. To identify the series resistors in a circuit, look for resistors that are connected in a straight line. 2.

Add the resistances of the series resistors.

To add the resistances of series resistors, simply add the individual resistance values together. For example, if you have two resistors with resistances of 10 ohms and 20 ohms, the total resistance of the series combination would be 10 + 20 = 30 ohms. 3.

Identify the parallel resistors.

Parallel resistors are resistors that are connected across each other, such that the same voltage is applied across each resistor. To identify the parallel resistors in a circuit, look for resistors that are connected in a "Y" shape. 4.

Calculate the reciprocal of the resistances of the parallel resistors.

To calculate the reciprocal of the resistances of parallel resistors, simply divide 1 by the individual resistance values. For example, if you have two resistors with resistances of 10 ohms and 20 ohms, the reciprocals of the resistances would be 1 / 10 = 0.1 and 1 / 20 = 0.05. 5.

Add the reciprocals of the parallel resistors.

To add the reciprocals of parallel resistors, simply add the individual reciprocal values together. For example, if you have two resistors with resistances of 10 ohms and 20 ohms, the total resistance of the parallel combination would be 0.1 + 0.05 = 0.15. 6.

Invert the result of step 5.

To find the total resistance of the parallel combination, simply invert the result of step 5. For example, if you have two resistors with resistances of 10 ohms and 20 ohms, the total resistance of the parallel combination would be 1 / 0.15 = 6.67 ohms. Here is an example of a series-parallel combination circuit: ``` R1 = 10 ohms R2 = 20 ohms R3 = 30 ohms R1 || R2 = (1 / 10) + (1 / 20) = 6 / 20 = 0.3 ohms R1 || R2 || R3 = (1 / 0.3) = 3.33 ohms ``` The total resistance of the circuit is 3.33 ohms.

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