A moving coil galvanometer needs a current of 100muA for a full scale deflecion of 50 divisions. If the resistance of the galvanometer is 1000 Omega, then its current senstivity is

Options

A. `5 xx 10^(6)"div"//A`
B. `5 xx 10^(5)"div"//A`
C. `10 xx 10^(5)"div"//A`
D. `15 xx 10^(6)"div"//A`

Explanation

To find the current sensitivity of the moving coil galvanometer, we can follow these steps:

### Step 1: Understand the formula for current sensitivity
Current sensitivity (S) of a galvanometer is defined as the change in deflection (in divisions) per unit change in current (in amperes). Mathematically, it can be expressed as:
\[ S = \frac{\Delta D}{\Delta I} \]
where \( \Delta D \) is the change in deflection and \( \Delta I \) is the change in current.

### Step 2: Identify the given values
From the problem, we know:
- The current required for full-scale deflection (I) = 100 µA = \( 100 \times 10^{-6} \) A
- The full-scale deflection in divisions (D) = 50 divisions

### Step 3: Calculate the current sensitivity
Using the values provided:
- The change in deflection \( \Delta D \) = 50 divisions
- The change in current \( \Delta I \) = 100 µA = \( 100 \times 10^{-6} \) A

Now, substituting these values into the formula for current sensitivity:
\[ S = \frac{\Delta D}{\Delta I} = \frac{50 \text{ divisions}}{100 \times 10^{-6} \text{ A}} \]

### Step 4: Simplify the calculation
\[ S = \frac{50}{100 \times 10^{-6}} = \frac{50}{0.0001} = 500000 \text{ divisions/A} \]

### Step 5: Express the result in scientific notation
\[ S = 5 \times 10^{5} \text{ divisions/A} \]

### Conclusion
The current sensitivity of the moving coil galvanometer is \( 5 \times 10^{5} \) divisions per ampere.

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