The range of a voltmeter of resistance `500 Omega` is 10V. The resistance to be connected to convert it into an ammeter of range 10 A is-

Options

A. `1 Omega` is parallel
B. `1 Omega` in series
C. `0.1 Omega` in parallel
D. `0.1 Omega` in series.

Explanation

To convert a voltmeter into an ammeter, we need to connect a shunt resistance in parallel with the voltmeter. Let's solve the problem step by step.

### Step 1: Identify the given values
- Resistance of the voltmeter (R_v) = 500 Ω
- Maximum voltage (V_max) = 10 V
- Desired maximum current (I_max) = 10 A

### Step 2: Calculate the current through the voltmeter (I_g)
Using Ohm's law, we can find the current that flows through the voltmeter when it is at its maximum voltage:
\[ I_g = \frac{V_{max}}{R_v} \]
Substituting the values:
\[ I_g = \frac{10 \, \text{V}}{500 \, \Omega} = 0.02 \, \text{A} \]

### Step 3: Determine the current flowing through the shunt resistor (I_s)
The total current (I_total) that we want to measure is 10 A. The current through the shunt resistor (I_s) can be calculated as:
\[ I_s = I_{max} - I_g \]
Substituting the values:
\[ I_s = 10 \, \text{A} - 0.02 \, \text{A} = 9.98 \, \text{A} \]

### Step 4: Calculate the shunt resistance (R_s)
The voltage across the shunt resistor (R_s) is the same as the voltage across the voltmeter when it is at its maximum voltage. Using Ohm's law again, we can express the relationship as:
\[ V_{max} = I_s \cdot R_s \]
Rearranging gives:
\[ R_s = \frac{V_{max}}{I_s} \]
Substituting the values:
\[ R_s = \frac{10 \, \text{V}}{9.98 \, \text{A}} \approx 1.002 \, \Omega \]

### Step 5: Round the shunt resistance
Since we typically use standard resistor values, we can round this to the nearest standard value. The closest standard resistor value is 1 Ω.

### Conclusion
The resistance to be connected to convert the voltmeter into an ammeter of range 10 A is approximately **1 Ω**.

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