To convet a `800 mV` range milli voltmeter of resistance `40 Omega` into a galvanometer of 100 mA` range, the resistance to be connected as shunt is

Options

A. `10 Omega`
B. `20 Omega`
C. `30 Omega`
D. `40 Omega`

Explanation

To convert an 800 mV range milli voltmeter with a resistance of 40 Ω into a galvanometer of 100 mA range, we need to calculate the shunt resistance to be connected. Here’s the step-by-step solution:

### Step 1: Understand the given values
- The initial voltage range of the milli voltmeter (V_G) = 800 mV = 800 × 10^(-3) V
- The resistance of the milli voltmeter (R_G) = 40 Ω
- The desired current range (I) = 100 mA = 100 × 10^(-3) A

### Step 2: Calculate the initial current (I_G) through the milli voltmeter
Using Ohm's Law:
\[ I_G = \frac{V_G}{R_G} \]
Substituting the values:
\[ I_G = \frac{800 \times 10^{-3}}{40} = 20 \times 10^{-3} \, \text{A} = 20 \, \text{mA} \]

### Step 3: Use the formula for shunt resistance
The relationship between the current ranges and resistances is given by:
\[ \frac{I}{I_G} = 1 + \frac{R_G}{R_S} \]
Where:
- \( I \) is the desired current (100 mA)
- \( I_G \) is the current through the milli voltmeter (20 mA)
- \( R_G \) is the resistance of the milli voltmeter (40 Ω)
- \( R_S \) is the shunt resistance we need to find

### Step 4: Substitute the known values into the formula
Substituting the values we have:
\[ \frac{100 \times 10^{-3}}{20 \times 10^{-3}} = 1 + \frac{40}{R_S} \]

### Step 5: Simplify the equation
Calculating the left side:
\[ 5 = 1 + \frac{40}{R_S} \]

### Step 6: Rearranging the equation
Subtract 1 from both sides:
\[ 4 = \frac{40}{R_S} \]

### Step 7: Solve for \( R_S \)
Now, multiply both sides by \( R_S \):
\[ 4R_S = 40 \]
Dividing both sides by 4:
\[ R_S = \frac{40}{4} = 10 \, \Omega \]

### Conclusion
The shunt resistance to be connected is **10 Ω**.

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