Electrics & Electronics: Electrical Principles: Circuits & measurement
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Parallel circuit resistance

Summary
Total resistance in a parallel circuit is found by adding the reciprocals of each resistance, then turning the answer back up the way it was.

Say you have a 12 volt parallel circuit with three branches, each with a 12 ohm resistor, and a current flow of 3 amperes. If you add another 12 ohm resistor to the circuit it produces an effect which is the opposite of what might be expected. Current increases from 3 amperes to 4.

This is because, in a parallel circuit, adding more branches provides more pathways, but decreases the overall circuit resistance, so current flow increases.

Total resistance of a parallel circuit is found by turning all the resistances upside down, to make fractions called reciprocals. In this case, each 12 becomes 1/12th.

The 4/12ths are added together, and the answer turned back up the way it was, so that it is 12/4, or 12 divided by 4, which equals 3. 3 ohms is therefore the total resistance in the circuit. Ohm’s law confirms the ammeter reading of 4 amperes. Now, if 2 resistors are removed, what is the result?

1/12th plus 1/12th is 2/12th’s, which, turned back the way it was, is 12 over 2, or 6 ohms. Voltage across the components is still 12 volts, but by Ohm’s law, the new current is 2 amperes. So removing the resistors, in this circuit, halves the current.