An ammeter, voltmeter and a resistor are connected in series to a cell and the readings are noted as I and V. If another resistor R is connected in parallel with a voltmeter, then

Options

A. I and V increase
B. I increases
C. I and V will remain same
D. I decreases

Answer

To solve the problem step by step, we will analyze the situation where an ammeter, voltmeter, and a resistor are connected in series to a cell, and then we will consider the effect of connecting another resistor in parallel with the voltmeter.

### Step 1: Understand the Initial Setup
We have an ammeter (A), a voltmeter (V), and a resistor (R1) connected in series to a cell. The readings of the ammeter and voltmeter are noted as I (current) and V (voltage across the voltmeter), respectively.

### Step 2: Analyze the Circuit
In a series circuit, the total resistance (R_total) is the sum of the individual resistances. Therefore, the total resistance in the circuit is:
\[ R_{\text{total}} = R_1 + R_V \]
where \( R_V \) is the internal resistance of the voltmeter.

### Step 3: Apply Ohm's Law
According to Ohm's Law, the current (I) flowing through the circuit can be expressed as:
\[ I = \frac{V_{\text{cell}}}{R_{\text{total}}} = \frac{V_{\text{cell}}}{R_1 + R_V} \]

### Step 4: Introduce the New Resistor
Now, when another resistor (R2) is connected in parallel with the voltmeter, the effective resistance of the voltmeter and the new resistor in parallel (R2) is given by:
\[ \frac{1}{R_{\text{eff}}} = \frac{1}{R_V} + \frac{1}{R_2} \]
This means that the effective resistance (R_eff) of the voltmeter and the resistor R2 will be less than the resistance of the voltmeter alone.

### Step 5: Calculate the New Total Resistance
The new total resistance in the circuit becomes:
\[ R_{\text{new}} = R_1 + R_{\text{eff}} \]
Since \( R_{\text{eff}} < R_V \), it follows that:
\[ R_{\text{new}} < R_1 + R_V \]

### Step 6: Determine the Effect on Current
Since the total resistance in the circuit has decreased, the current (I) flowing through the circuit will increase. According to Ohm's Law:
\[ I_{\text{new}} = \frac{V_{\text{cell}}}{R_{\text{new}}} \]
Since \( R_{\text{new}} < R_{\text{total}} \), we have:
\[ I_{\text{new}} > I \]

### Conclusion
Thus, when the resistor R2 is connected in parallel with the voltmeter, the current I increases. The voltage across the voltmeter remains the same because it is still connected across the same cell.

### Final Answer
When another resistor R is connected in parallel with the voltmeter, the current (I) in the circuit increases.

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