Q. 33

# How will you conclude that the same potential difference (voltage) exists across three resistors connected in a parallel arrangement to a battery?

The same potential difference exists across three resistors connected in a parallel arrangement to a battery can be concluded as follows:

1. Make a parallel combination of three resistors ×Y of three resistors R1, R2 and R3. Connect the resistors with a battery, an ammeter and a plug key.

2. Connect a voltmeter in parallel with the resistors.

3. Plug the key and note the ammeter reading and also note the voltmeter reading.

4. The potential difference across each resistor is V.

5. Now, take out the plug key from the circuit. Remove the ammeter and voltmeter from the given circuit.

6. Insert the ammeter in series with the resistor R1 and note down the ammeter reading I1.

7. Similarly, note the I2 and I3 across the resistors R2 and R3.

The total current through the circuit will be given by:

I = I1+I2+I3

Applying Ohm’s law to the parallel combination of resistors

I = V/ RP

For each resistor, ohm’s law will be given by:

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

Now, V/ RP = V/ R1+ V/ R2+ V/ R3

1/ RP = 1/ R1+ 1/ R2+ 1/ R3

Hence, the same potential difference exists across three resistors connected in a parallel arrangement to a battery.

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