If a voltmeter, in advertently mistaken for an ammeter, were inserted into the circuit, the current

Options

A. increases
B. remains same
C. decreases
D. becomes zero

Answer

To solve the problem, we need to analyze the effect of mistakenly inserting a voltmeter into a circuit in place of an ammeter. Here’s a step-by-step solution:

### Step 1: Understand the Circuit Configuration
Initially, we have a circuit with a voltage source (V) and a resistor (R). An ammeter (with low resistance, \( R_A \)) is connected in series to measure the current flowing through the circuit.

### Step 2: Calculate the Current with the Ammeter
Using Ohm's Law, the total resistance in the circuit when the ammeter is connected is:
\[ R_{\text{equivalent}} = R + R_A \]
The current (\( I \)) flowing through the circuit can be calculated as:
\[ I = \frac{V}{R_{\text{equivalent}}} = \frac{V}{R + R_A} \]

### Step 3: Replace the Ammeter with a Voltmeter
Now, we replace the ammeter with a voltmeter (with high resistance, \( R_V \)). The new total resistance in the circuit becomes:
\[ R_{\text{equivalent}}' = R + R_V \]

### Step 4: Analyze the Resistance Values
Since the resistance of the voltmeter (\( R_V \)) is very high compared to the resistance of the ammeter (\( R_A \)), we can conclude:
\[ R_{\text{equivalent}}' > R_{\text{equivalent}} \]
This means that the equivalent resistance of the circuit has increased when the voltmeter is used instead of the ammeter.

### Step 5: Calculate the New Current
The new current (\( I' \)) in the circuit with the voltmeter can be calculated as:
\[ I' = \frac{V}{R_{\text{equivalent}}'} = \frac{V}{R + R_V} \]

### Step 6: Compare the Currents
Since \( R_{\text{equivalent}}' > R_{\text{equivalent}} \), it follows that:
\[ I' < I \]
This indicates that the current has decreased when the voltmeter is used in place of the ammeter.

### Conclusion
Therefore, the current in the circuit decreases when a voltmeter is mistakenly inserted instead of an ammeter.

### Final Answer
The current would **decrease**.

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