A micrometer has a resistance of `10Omega` and a full scale range of `50muA`. It can be used as a voltmeter or a higher range ammeter provided a resistance combination (s).

Options

A. 50 V range with `10Omega` resistance in series
B. 10 V range with 200 `kOmega` resistance in series
C. 5 mA range with `1Omega` resistance in parallel
D. 10 mA range with 1 `kOmega` resistance in parallel.

Answer

To solve the problem step-by-step, we need to determine the resistance combinations required to convert the micrometer into a voltmeter and an ammeter.

### Given:
- Resistance of micrometer (G) = 10 Ω
- Full scale current (I_max) = 50 µA = 50 × 10^(-6) A

### Part 1: Converting Micrometer to Voltmeter

1. **Determine the voltage range for the voltmeter:**
- Let's say we want to convert it to a voltmeter with a full-scale range of 50V.

2. **Calculate the total resistance needed for the voltmeter:**
- The voltage (V) across the micrometer when it is at full scale can be calculated using Ohm's Law:
\[ V = I \times R \]
- For the micrometer:
\[ V = I_{max} \times R_{micrometer} = 50 \times 10^{-6} \times 10 = 0.0005 \, V = 0.5 \, mV \]

3. **Calculate the required resistance (R) to achieve 50V:**
- We need to find the resistance R such that:
\[ 50 = I_{max} \times (R + R_{micrometer}) \]
- Rearranging gives:
\[ R + 10 = \frac{50}{50 \times 10^{-6}} = 10^6 \, \Omega \]
- Therefore:
\[ R = 10^6 - 10 = 999990 \, \Omega \approx 1 \, M\Omega \]

### Conclusion for Voltmeter:
- The required resistance to convert the micrometer into a voltmeter with a full-scale range of 50V is approximately 1 MΩ.

### Part 2: Converting Micrometer to Ammeter

1. **Determine the current range for the ammeter:**
- Let's say we want to convert it to an ammeter with a full-scale range of 5 mA.

2. **Using the formula for current division in parallel:**
- The total current (I) through the circuit is the sum of the current through the micrometer and the current through the parallel resistor (R):
\[ I = I_{micrometer} + I_{R} \]
- The voltage across both components is the same:
\[ V = I_{micrometer} \times R_{micrometer} = I_{R} \times R \]

3. **Calculate the required resistance (R) for 5 mA:**
- For 5 mA:
\[ 5 \times 10^{-3} = 50 \times 10^{-6} + \frac{(5 \times 10^{-3} - 50 \times 10^{-6}) \times R}{10} \]
- Rearranging and solving for R gives:
\[ R = \frac{(5 \times 10^{-3} - 50 \times 10^{-6}) \times 10}{50 \times 10^{-6}} = 0.1 \, \Omega \]

### Conclusion for Ammeter:
- The required resistance to convert the micrometer into an ammeter with a full-scale range of 5 mA is approximately 0.1 Ω.