Activity . Make a parallel combination, XY, of three resistors having resistances R , R , and R , respectively. Connect it with a battery, a plug key and an ammeter, as shown in Fig. .
. Also connect a voltmeter in parallel with the combination of resistors. Plug the key and note the ammeter reading. Let the current be I .
Also take the voltmeter reading. It gives the potential difference V, across the combination. The potential difference across each resistor is also V . This can be checked by connecting the voltmeter across each individual resistor (see Fig.
. ). Figure . Figure .
Figure . Figure . Figure . Take out the plug from the key.
Remove the ammeter and voltmeter from the circuit. Insert the ammeter in series with the resistor R , as shown in Fig. . .
Note the ammeter reading, I . Figure . Figure . Figure .
Figure . Figure . Similarly, measure the currents through R and R . Let these be I and I , respectively.
What is the relationship between I , I , I and I ? It is observed that the total current I , is equal to the sum of the separate currents through each branch of the combination. I = I + I + I ( . ) Let R p be the equivalent resistance of the parallel combination of resistors.
By applying Ohm’s law to the parallel combination of resistors, we have I = V/R p ( . ) On applying Ohm’s law to each resistor, we have I = V /R ; I = V /R ; and I = V /R ( . ) From Eqs. ( .
) to ( . ), we have V/R p = V/R + V/R + V/R or /R p = /R + /R + /R ( . ) Thus, we may conclude that the reciprocal of the equivalent resistance of a group of resistances joined in parallel is