An ammeter and a voltmeter are joined in sereis to a cell. Their readings are `A` and `V` respectively. If a resistance is now joinding parallel with the voltmeter. Then

Options

A. Both A and V will decrease
B. Both A and V will increase
C. A will decrease, V will increase
D. A will increase, V will decrease

Answer

To solve the problem step by step, we need to analyze the situation when a resistance is connected in parallel with a voltmeter that is already in series with an ammeter and a cell.

### Step 1: Understand the Initial Setup
Initially, we have an ammeter (A) and a voltmeter (V) connected in series with a cell. The ammeter measures the current flowing through the circuit, and the voltmeter measures the voltage across its terminals.

### Step 2: Identify the Effect of Adding a Resistance in Parallel
When a resistance (R) is connected in parallel with the voltmeter, the overall resistance of the circuit changes.

### Step 3: Calculate the New Equivalent Resistance
- The equivalent resistance of the voltmeter and the parallel resistance can be calculated using the formula for resistors in parallel:
\[ R_{eq} = \frac{R_v \cdot R}{R_v + R} \]
where \( R_v \) is the resistance of the voltmeter.

- Since this new equivalent resistance \( R_{eq} \) is less than the resistance of the voltmeter alone, the total resistance of the circuit decreases.

### Step 4: Analyze the Current Flow
- According to Ohm's Law, if the total resistance of the circuit decreases, the total current flowing through the circuit (I) will increase. This means the reading on the ammeter (A) will increase.

### Step 5: Analyze the Voltage Across the Voltmeter
- The voltmeter measures the voltage across its terminals. With the new parallel resistance, some current will flow through the resistance R instead of the voltmeter.

- The voltage across the voltmeter can be expressed as:
\[ V = I \cdot R_v \]
However, since some current is now diverted through the parallel resistance, the effective current through the voltmeter will decrease.

### Step 6: Conclusion on Readings
- Therefore, the reading of the ammeter (A) will increase due to the decrease in total resistance.
- The reading of the voltmeter (V) will decrease because the effective current through the voltmeter has decreased.

### Final Answer
- The ammeter reading increases (A increases) and the voltmeter reading decreases (V decreases).