# Electricity | Activities in Text Book with Solution

Activity 12.6

Make a parallel combination, XY, of three resistors having resistances R1, R2, and R3, respectively. Connect it with a battery, a plug key and an ammeter, as shown in Fig. 12.10. Also connect a voltmeter in parallel with the combination of resistors.

 Fig. 12.10

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. 12.11).

Take out the plug from the key. Remove the ammeter and voltmeter from the circuit. Insert the ammeter in series with the resistor R1, as shown in Fig. 12.11. Note the ammeter reading, I1.

Figure 12.11

Similarly, measure the currents through R2 and R3. Let these be I2 and I3, respectively.
What is the relationship between
I, I1, I2 and I3?

✅ Answer: It is observed that the total current I, is equal to the sum of the separate currents through each branch.

I = I1 + I2 + I3

Let Rp be the equivalent resistance of the parallel combination of resistors.

Hence, I = V/Rp

On applying Ohm’s law to each resistor, we have

I1 = V /R1             I2 = V /R2             I3 = V /R3

V/Rp = V/R1 + V/R2 + V/R3

or

1/Rp = 1/R1 + 1/R2 + 1/R3

Thus, the reciprocal of the equivalent resistance of a group of resistances joined in parallel is equal to the sum of the reciprocals of the individual resistances.