What is the relation between Galvanometer sensitivity and the shunt $R$? Okay, it may be a weird question, but really I'm still confused with the relation between them, why we add the shunt? and what happens to it when we change the sensitivity?, and i get more and more confusion, especially when I find a question like

The resistance of the coil of galvanometer (R), so the shunt resistance when the sensitivity decreases to its quarter is ...... .

and the answer is $ R/3$ !! can someone explain to me the idea of the galvanometer in simple words?  
 A: The galvanometer measures dc current, so if you want to know what the current is in a branch you have to break the line and connect the leads in series. Ideally, it has zero internal resistance to ensure that its presence has no effect on the circuit measured. Also if the internal resistance is really zero than so is the dissipated power internally in the meter. 
In practice, there is always some internal resistance that limits the maximum current you can measure. If you want to measure higher current then you can connect a shunt resistor in parallel with the meter and have the two in series with the rest of the circuit. The two together (internal and shunt) will assure that a current smaller than the meter's limit will flow through it.
A: Galvanometers are characterized by


*

*Sensitivity - Current which will cause full-scale deflection = $I_{FSD}$

*Resistance - Resistance of the moving-coil = R


You are not given much.

The resistance of the coil of galvanometer (R), so the shunt resistance when the sensitivity decreases to its quarter is ...... .

To achieve $\frac {1}{4}$ Sensitivity, you must have $\frac {1}{4}$ deflection or $\frac {1}{4}$ of $I_{FSD}$.  This means the total resistance of the shunt and galvanometer must be 25% of galvanometer resistance. 
4 $\times\ I_{FSD}$ would have to go into combination to give full-scale deflection of galvanometer.
The ratio of the resistances means $\frac {3}{4}$ of current goes through shunt and $\frac {1}{4}$ through the meter movement.
Rest is just math:
$$\frac {1}{R_T} = \frac {1}{R_{Gal}} + \frac {1}{R_{SH}}$$
