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.