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/ R_P

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

I₁ = V/ R₁ ;I₂ = V/ R₂ ;I₃ = V/ R₃

Now, V/ R_P = V/ R₁+ V/ R₂+ V/ R₃

1/ R_P = 1/ R₁+ 1/ R₂+ 1/ R₃

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