Total resistance of equal resistors in a parallel circuit is equal to the resistance of one resistor divided by the number of resistors.

where

R_{T} = total resistance

R = resistance of one resistor

N = number of resistors

**Example:**

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

Solution :

R1 = R2 = R3 = R4 = R5 = 40Ω

So, N = 5

R_{T} = R / N = 40/5 = 8 Ω

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 below equation.

Above equation, this is valid when there are only two resistors in parallel.

**Example:**

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

Solution :

R_{T} = (12 x 4) / (12+4) = 48/16 = 3 Ω

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 above equation 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 8Ω resistor to provide a total resistance of 6Ω (Figure 28)?

Figure 28 Example Parallel Circuit

Solution :

Rx = (R_{T} .R) / (R – R_{T} ) = (8×6)/(8+6) = 48/2 = 24 Ω

Rt= 2k R= 1.2k

Rx = (Rt.R)/(R-Rt)

(2k .1.2k)/(1.2k – 2k)

(2000 . 1200)/(1200 – 2000)

2,400,000/ -800

= -3k…………?

So my resistor will actually be a superconductor?

Silly Herman. When you have two parallel resistors, you can’t have a total resistance that is greater than either of the two parallel resistors…..