As, (R+G) x ig = V(R+G) = V/ig = 3/30 x 16 x 10^−6 = 6.25 kΩ Therefore, Value of R is nearly equal to 6 kΩ.

I think the answer should be 6250 firstly we can calculate current by unitary method then apply ohms law

Galvanometer Conversion

To convert a galvanometer into a voltmeter, we need to connect it in parallel with a suitable resistor. This resistor is known as the shunt resistance.

Formula
The formula to calculate the shunt resistance is given by:

Rshunt = (Vg / I) - Rg

Where:
- Rshunt is the shunt resistance
- Vg is the desired voltage range
- I is the full-scale deflection current of the galvanometer
- Rg is the resistance of the galvanometer

Given Data
- Number of divisions on the galvanometer (n) = 30
- Sensitivity of the galvanometer (S) = 16 uA/div
- Desired voltage range (Vg) = 3V

Calculating Full-Scale Deflection Current (I)
The full-scale deflection current can be calculated by multiplying the sensitivity with the number of divisions:

I = S * n

I = 16 uA/div * 30 = 480 uA

Calculating Resistance of the Galvanometer (Rg)
To calculate the resistance of the galvanometer, we need to know the voltage across it and the current flowing through it.

Calculating Shunt Resistance (Rshunt)
Using the formula mentioned earlier, we can calculate the shunt resistance required to convert the galvanometer into a voltmeter.

Rshunt = (Vg / I) - Rg

Rshunt = (3V / 480 uA) - Rg

Now, we need to choose a value for Rg that ensures the desired range of 3V is achieved. Let's assume a value of Rg = 1 Ω.

Rshunt = (3V / 480 uA) - 1 Ω

Rshunt = 6250 Ω - 1 Ω

Rshunt ≈ 6249 Ω

Therefore, to convert the galvanometer into a voltmeter to read 3V, we need to connect a shunt resistance of approximately 6249 ohms in parallel with the galvanometer.