Solution:

Initial Setup:

1. An ammeter and a voltmeter are connected in series to a cell.
2. The ammeter reading is
   $A$ 

   (current through the circuit).

3. The voltmeter reading is
   $V$ 

   (potential difference across the cell).

What Happens When a Resistance is Added in Parallel with the Voltmeter?

• The voltmeter has a high internal resistance (
  $R_v$ 

  ) to minimize current flow through it.

• When an additional resistance (
  $R$ 

  ) is connected in parallel with the voltmeter, the effective resistance of the voltmeter decreases because: $$R_{\text{eff}} = \frac{R_v \cdot R}{R_v + R}.$$ 

  Since $R$ 

  is finite, $R_{\text{eff}} < R_v$ 

  .

Effect on the Circuit:

1. Decrease in total resistance:
   • The voltmeter (and its parallel combination) is in series with the ammeter.
   • The decrease in
     $R_{\text{eff}}$ 

     reduces the total resistance of the circuit.

   • Lower resistance means higher total current through the circuit (Ohm's law:
     $I = \frac{V}{R_{\text{total}}}$ 

     ).

   • Thus, the ammeter reading (
     $A$ 

     ) increases.

2. Voltage across the voltmeter decreases:
   • With the reduced effective resistance of the voltmeter, a smaller fraction of the total voltage is dropped across it.
   • Hence, the voltmeter reading (
     $V$ 

     ) decreases.

Conclusion:

When a resistance is added in parallel with the voltmeter:

• The ammeter reading (
  $A$ 

  ) increases.

• The voltmeter reading (
  $V$ 

  ) decreases.