With the help of a labelled circuit diagram derive a formula to find combined resistance (R) when two or more resistances ( R 1 , R 2 , R 3 . . . . . . . . ) are connected in parallel taking symbols potential difference (V) and current (I).

Consider resistances R 1 , R 2 , R 3 .... R n are connected in parallel with potential difference V . Let I be the current flows in the circuit as shown in the following diagram. Let I 1 , I 2 , I 3 ..... I n be the current flowing through the resistances R 1 , R 2 , R 3 ..... R n resistors respectively. I=I1+I2= According to ohm's law I 1 = V R 1 , I 2 = V R 2 , I 3 = V R 3 ......... I n = V R n But total current in the circuit is I = I 1 + I 2 + I 3 + . . . . . . + I n Since potential difference across each resistance in the parallel circuit is same V R e q = V R 1 + V R 2 + V R 3 + . . . + V R n ( R e q is the equivalent resistance in the circuit) The equivalent resistance in the circuit is given by 1 R e q = 1 R 1 + 1 R 2 + 1 R 3 + . . . + 1 R n Note: The net resistance in the parallel circuit decreases.