Total resistance of equal resistors in a parallel circuit is equal to the resistance of one resistor

divided by the number of resistors.

Where

Example: Five lamps, each with a resistance of 40, are connected in parallel. Find total resistance.

When any two resistors are unequal in a parallel circuit, it is easier to calculate R_T by multiplying the two resistances and then dividing the product by the sum, as shown in equation (2-11). As shown in equation (2-11), this is valid when there are only two resistors in parallel.

Example: Find the total resistance of a parallel circuit which has one 12 and one 4 resistor.

In certain cases involving two resistors in parallel, it is useful to find an unknown resistor, R_X, to obtain a certain R_T. To find the appropriate formula, we start with equation (2-10) and let the known resistor be R and the unknown resistor be R_X.

Example: What value of resistance must be added, in parallel, with an 8 resistor to provide a total resistance of 6 (Figure 28)?

Figure 28 Example Parallel Circuit

Solution: