Analysis:

To determine the resistance needed to be connected in series with the coil of the moving coil galvanometer, we need to consider the current sensitivity and voltage sensitivity of the galvanometer.

Current Sensitivity:

The current sensitivity of the galvanometer is given as 10 divisions per milliampere. This means that for every milliampere of current passing through the galvanometer, the pointer will move 10 divisions. We can represent this mathematically as:

Current sensitivity = ΔI / Δd

where ΔI is the change in current and Δd is the change in divisions.

Voltage Sensitivity:

The voltage sensitivity of the galvanometer is given as 2 divisions per millivolt. This means that for every millivolt of voltage applied across the galvanometer, the pointer will move 2 divisions. We can represent this mathematically as:

Voltage sensitivity = ΔV / Δd

where ΔV is the change in voltage and Δd is the change in divisions.

Required Resistance:

We want each division to read 1 volt on the galvanometer. This means that for every change of 1 volt, the pointer should move 1 division. Mathematically, this can be represented as:

Voltage sensitivity = 1V / 1 division

Now, we can equate the voltage sensitivities:

2 divisions/millivolt = 1V / 1 division

Simplifying this equation, we can calculate the change in voltage:

1V = 2 * 1 millivolt

1V = 2 * 0.001V

1V = 0.002V

Calculating the Resistance:

To calculate the resistance needed to be connected in series with the coil of the galvanometer, we can use Ohm's law:

V = IR

where V is the voltage, I is the current, and R is the resistance.

In this case, the voltage is 0.002V and the current sensitivity is 10 divisions per milliampere. Converting the current sensitivity to amperes:

10 divisions/milliampere = 10 * 0.001A/division

10 divisions/milliampere = 0.01A/division

Substituting the values into Ohm's law equation:

0.002V = 0.01A/division * R

Simplifying the equation, we can solve for R:

R = 0.002V / (0.01A/division)

R = 0.002V * (division/0.01A)

R = 0.002V * 100 division/A

R = 0.2 ohms

Therefore, a resistance of 0.2 ohms needs to be connected in series with the coil of the moving coil galvanometer in order for each division to read 1 volt.