Electrical Calculations - Basic Mathematics for Water and Wastewater Operators - page 157

Invert both sides of the equation to solve for R T :

8
7

R T == 114 . ohms

Note: When resistances are connected in parallel, the total resistance is always
less than the smallest resistance of any single branch.

p roduCt over the s uM M ethod
When any two unequal resistors are in parallel, it is often easier to calculate the total
resistance by multiplying the two resistances and then dividing the product by the
sum of the resistances:

RR
RR

×
+

1 2

R

T =

(10.17)

2

1

where R T is the total resistance in parallel, and R 1 and R 2 are the two resistors in
parallel.

■ Example 10.25
Problem: What is the equivalent resistance of a 20-ohm and a 30-ohm resistor con-
nected in parallel?

Solution:
Given:
R 1 = 20 ohms
R 2 = 30 ohms

RR
RR

×
+

20 ×

+

30

1 2

R

T =

= = 12 ohms

20 30

1 2

p oWer in p arallel C irCuits
As in the series circuit, the total power consumed in a parallel circuit is equal to the
sum of the power consumed in the individual resistors.

Note: Because power dissipation in resistors consists of a heat loss, power dissipa-
tions are additive regardless of how the resistors are connected in the circuit.

P T = P 1 + P 2 + P 3 + … + P n (10.18)

where P T is the total power, and P 1 , P 2 , P 3 , … P n are the branch powers.
Total power can also be calculated by the following equation:

P T = E × I T (10.19)