galvanometer TO voltmeter AND ammeter conversion

galvanometer

A galvanometer is a type of sensitive ammeter: an instrument for detecting electric current. It is an analog electromechanical actuator that produces a rotary deflection of some type of pointer in response to electric current through its coil in a magnetic field

D'Arsonval/Weston galvanometer movement - with the moving coil 

 shown in orange

Galvanometer to Voltmeter Conversion

Now our interest is to convert a galvanometer to voltmeter to measure the potential difference across any component in a circuit. This can be done by adding a suitable high resistance in series with galvanometer. When high resistance is connect in series with the galvanometer, very negligible current flow through it.

The figure show a galvanometer G connected in series with high resistor R across a component in the circuit. We are interested to know the potential difference Δ V across the component. If I is the maximum current through the galvanometer then according ohms law

Δ V = (R +G) I.  

Here R is the resistance that is connected in series with galvanometer resistance G. From the above equation

(R +G) = ΔVI

Resistance that is to be connected in series is
R = ΔVI - G

Now we will decide what would be the value of the resistance that is connected in series with the galvanometer. Let’s say we need a voltmeter of to measure voltage between 0 -10V, and we have galvanometer specifying that its resistance is 20ohms and maximum permissible current is 0.1mA.

             R = 10V0.1×10−3 - 20 Ω
                = 99980 Ω
                ≃ 100k ω.

The high resistance needed is ≃ 100kΩ. We can build any range of voltmeter by suitable high resistance in series to the galvanometer. 

CONVERSION OF GALVANOMETER INTO AMMETER
Since Galvanometer is a very sensitive instrument therefore it can’t measure heavy currents. In order to     convert a Galvanometer into an Ammeter, a very low resistance known as "shunt" resistance is     connected in parallel to Galvanometer. Value of shunt is so adjusted that most of the current passes     through the shunt. In this way a Galvanometer is converted into Ammeter and can measure heavy     currents without fully deflected.
VALUE OF SHUNT RESISTANCE
Let resistance of galvanometer = Rg and it gives full-scale deflection when current Ig is passed through     it. Then,
Vg = IgRg -------(i)
Let a shunt of resistance (Rs) is connected in parallel to galvanometer. If total current through the     circuit is I.
Then current through shunt:
Is = (I-Ig)
potential difference across the shunt:
Vs= IsRs
or               Vs = (I – Ig)Rs -------(ii)
But
Vs =Vg (I - Ig)Rs = IgRg