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# Resistors in Parallel

Author: E.E. Kimberly

 Fig. 3-4. Resistors in Parallel

If two or more resistors be connected in parallel, the voltage drop across every one will be the same. The current in each resistor may be calculated by Ohm's Law. The total current in the combination will be the sum of the currents in all the resistors. Thus, in Fig. 3-4,

or

(3-3)

The reciprocals of the resistances, or

are called the conductances of the branches 1, 2, 3, and 4, respectively.

In solving for the line current, the resistances of all resistors may be combined into an equivalent single resistance. The reciprocal of the equivalent single resistance is equal to the sum of the reciprocals of the resistances in parallel. Let R = the equivalent single resistance. Then,

Hence,

(3-4)

The value of 1/R is the conductance of the whole parallel group. Thus, the conductance of the group is equal to the sum of the conductances of the individual resistors.

Example 3-3. - Connected in parallel to a 230-volt line, as indicated in Fig. 3-4, are four resistors having the following resistances: R1 = 50 ohms, R2 = 10 ohms, R3 = 15 ohms, R4 = 40 ohms. Find the current I in the line.

First Solution. - In this case,

I = I1 + I2 + I3 + I4

Also,

I1 = V/R1 = 230/50 = 4.6 amp
I2 = V/R2 = 230/10 = 23 amp
I3 = V/R3 = 230/15 = 15.33 amp
I4 = V/R4 = 230/40 = 5.75 amp

Therefore,

I = 4.6 + 23 + 15.33 + 5.75 = 48.68 amp

Second Solution. - The conductance of the entire group of resistors is

The line current is

Last Update: 2010-10-05