How to simplify circuits with resistors

1. In any given circuit first of all recognize the resistances connected in series then by summing the individual resistances draw a new, simplified circuit diagram.

For series combination of resistances equivalent resistance is given by the equation
Req= R1 + R2+R3
The current in each resistor is the same when connected in parallel combination.

2. Then recognize the resistances connected in parallel and find the equivalent resistances of parallel combinations by summing the reciprocals of the resistances and then taking the reciprocal of the result. Draw the new, simplified circuit diagram.
(1/R)=(1/R1)+(1/R2)+(1/R2)

Remember that for resistors connected in parallel combination ‘The potential difference across each resistor is the same’.

3. Repeat the first two steps as required, until no further combinations can be made using resistances. If there is only a single battery in the circuit, this will usually result in a single equivalent resistor in series with the battery.

4. Use Ohm’s Law, V= IR, to determine the current in the equivalent resistor. Then work backwards through the diagrams, applying the useful facts listed in step 1 or step 2 to find the currents in the other resistors. (In more complex circuits, Kirchhoff’s rules can be applied).

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