
Basic Circuit Analysis Parallel Circuits
Section 22 Voltage in Parallel Circuits Recall a Definition A parallel circuit has more than one path for current flow.  Equation Total Resistance of a Parallel Circuit R_{T} =  1  1  +  1  +  1  + ... +  1  R_{1}  R_{2}  R_{3}  R_{n}  Where  R_{T} = Total resistance of the parallel circuit
 R_{1}, R_{2}, R_{3}, R_{n} = Resistance of the individual resistors
 This formal equation for the total resistance of a parallel circuit looks horribly complicated ... at least at first glance. In the days of pencilandpaper calculation, this equation was generally considered impossible to use. With today's calculator technology, the 1/x function key renders the process of solving the parallel resistance equation fairly straightforward. Example Suppose there is a parallel resistor circuit with values of 10W, 15W, and 25W. 1. Set up the equation: R_{T} =  1  1  +  1  +  1  R_{1}  R_{2}  R_{3}  2.Subsititue the given values R_{T} =  1  1  +  1  +  1  10  15  25  3. Solve with keystrokes: 10 1/x + 15 1/x + 25 1/x = 1/x 4.838709677 4. Present the solution: R_{T }= 4.8W More Examples Endless Examples & Exercises Given the value of all the resistors in a parallel circuit, calculate the total resistance. Do these exercises until you are confident you can handle them.   In practical electronic design and troubleshooting, it is sometimes necessary to adjust the total resistance of a parallel circuit. Suppose, for instance, a circuit is a simple 180W resistor. For some good reason, you fine it necessary to lower the resistance to 120W by adding another resistor in parallel. The problem, of course, is to determine the value of that resistor. Using the productoversum equation, you are given the desired total resistance (R_{T}) and the value of one of the two resistors (R_{1}). Solve the equation for R_{2}. Procedure 1. Begin with the productoversum equation: R_{T} =  R_{1}R_{2}  R_{1} + R_{2}  2. Solve it for R_{2}: R_{2} =  R_{T}R_{1}  R_{1} – R_{T}  3. Substitute the known values and do the math: R_{2} =  (120)(180)  =360  180 – 120  4. Present the solution: R_{2} = 360W Some Notes About Parallel Resistance  The total resistance of a parallel circuit is always less than the value of the smallest resistor.
 When all resistors in a parallel circuit have the same value, the total resistance is equal to the common value divided by the number of resistors. Example: Three 330W resistors in parallel provide a total resistance of 110W.

When a resistor is removed from a parallel circuit, (1) current continues to flow through the remaining resistors, and (2) the total resistance increases 
When a resistor is shorted in a parallel circuit, the total resistance falls to zero. .
