A moving coil galvanometer has 150 equal divisions. Its current sensitivity is 10 division per milliampere and voltage sensitivity is 2 divisions per millivolt. In order that each division reads 1 volt, the resistance in ohms needed to be connected in series with the coil will be

Options

A. 99995
B. 9995
C. `10^(3)`
D. `10^(5)`

Explanation

To solve the problem, we need to determine the resistance that must be connected in series with a moving coil galvanometer in order for each division to read 1 volt. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Given Information
- The galvanometer has 150 equal divisions.
- Current sensitivity (C.S) = 10 divisions per milliampere.
- Voltage sensitivity (V.S) = 2 divisions per millivolt.

### Step 2: Calculate the Resistance of the Galvanometer
We know that the relationship between voltage sensitivity, current sensitivity, and the resistance of the galvanometer (G) is given by:
\[ V.S = \frac{C.S}{G} \]
Rearranging this gives us:
\[ G = \frac{C.S}{V.S} \]
Substituting the values:
\[ G = \frac{10 \text{ divisions/mA}}{2 \text{ divisions/mV}} = \frac{10}{2} = 5 \, \text{ohms} \]

### Step 3: Determine the Full Scale Deflection Current (I_G)
The full-scale deflection current (I_G) can be calculated using the total number of divisions and the current sensitivity:
\[ I_G = \frac{\text{Total divisions}}{\text{C.S}} = \frac{150 \text{ divisions}}{10 \text{ divisions/mA}} = 15 \, \text{mA} \]

### Step 4: Calculate the Required Voltage
To ensure that each division reads 1 volt, the total voltage (V) needed for 150 divisions is:
\[ V = 150 \text{ divisions} \times 1 \text{ volt/division} = 150 \, \text{volts} \]

### Step 5: Use Ohm's Law to Find the Total Resistance
According to Ohm's Law, the total resistance (R_total) needed in the circuit can be calculated as:
\[ R_{\text{total}} = \frac{V}{I_G} \]
Substituting the values:
\[ R_{\text{total}} = \frac{150 \text{ volts}}{15 \times 10^{-3} \text{ A}} = \frac{150}{0.015} = 10000 \, \text{ohms} \]

### Step 6: Calculate the Required Series Resistance (R)
The total resistance in the circuit is the sum of the galvanometer resistance (G) and the series resistance (R):
\[ R_{\text{total}} = R + G \]
Rearranging gives:
\[ R = R_{\text{total}} - G \]
Substituting the values:
\[ R = 10000 \, \text{ohms} - 5 \, \text{ohms} = 9995 \, \text{ohms} \]

### Final Answer
The resistance that needs to be connected in series with the galvanometer is:
\[ \boxed{9995 \, \text{ohms}} \]