P ARALLEL The current through a single resistor R across which there is a potential difference V is given by Ohm’s law I = V/R . Resistors are sometimes joined together and there are simple rules for calculation of equivalent resistance of such combination. FIGURE . A series combination of two resistor R and R .
Two resistors are said to be in series if only one of their end points is joined (Fig. . ). If a third resistor is joined with the series combination of the two (Fig.
. ), then all three are said to be in series. Clearly, we can extend this definition to series combination of any number of resistors. FIGURE .
A series combination of three resistors R , R , R . Two or more resistors are said to be in parallel if one end of all the resistors is joined together and similarly the other ends joined together (Fig. . ).
FIGURE . Two resistors R and R connected in parallel. Consider two resistors R and R in series. The charge which leaves R must be entering R .
Since current measures the rate of flow of charge, this means that the same current I flows through R and R . By Ohm’s law: Potential difference across R = V = I R , and Potential difference across R = V = I R . The potential difference V across the combination is V + V . Hence, V = V + V = I ( R + R ) ( .
) This is as if the combination had an equivalent resistance R eq , which by Ohm’s law is R eq I ≡ = ( R + R ) ( . ) If we had three resistors connected in series, then similarly V = I R + I R + I R = I ( R + R + R ). ( . ) This