Resistance in Parallel:

Total resistance in a parallel circuit could be found through applying Ohm's Law. Divide of the voltage across the parallel resistance through the total line current as display in the given equation (2-9).

R_T = V/ I_T                                                         (2-9)

Example: Find out the total resistance of the circuit display in Figure if the line voltage is 120 V and total current is 26A.

R_T = V/ I_T = 120/26 =4.62 ?

The total load connected to a 120 V source is the similar as the one "equivalent resistance" of 4.62 ? which was connected across the source display in the given figure.   Equivalent resistance is the total resistance a combination of loads present to a circuit.

Figure: Equivalent Resistance in a Parallel Circuit

The total resistance in a parallel circuit could also be found through using the equation (2-10).

1/R_T =1/R₁ +1/R₂₊1/R₃ + ... 1/R_N                       (2-10)

Example: Find the total resistance of a 4 ?, an 8 ?, and a 16? resistor in parallel (Figure 27).

Figure: Total Resistance in a Parallel Circuit

Solution:

1/R_T =1/R₁ +1/R₂₊1/R₃

1/R_T =1/4 +1/8₊1/16

1/R_T =4/16 +2/16₊1/16 = 7/16

R_T =16/7 = 2.29?

Note:   Every time you like resistors are in parallel, the total resistance is always smaller than any single branch.