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Resistors in ParallelAuthor: E.E. Kimberly
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. 34, or (33) 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,(34) 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 33.  Connected in parallel to a 230volt line, as indicated in Fig. 34, are four resistors having the following resistances: R_{1} = 50 ohms, R_{2} = 10 ohms, R_{3} = 15 ohms, R_{4} = 40 ohms. Find the current I in the line.
First Solution.  In this case, I = I_{1} + I_{2} + I_{3} + I_{4} Also,
I_{1} = V/R_{1} = 230/50 = 4.6 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


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