Electricity & Megnetism

Ammeter and voltmeter

An ammeter is an electrical device which is used to measure the current. It is the modified form of the galvanometer. It is a low resistance galvanometer. It is always connected in series with the circuit to measure current. An ideal ammeter has zero resistance.ammeter

Meter movement

The portion of galvanometer whose motion causes the needle of the device to move across the scale is usually known as meter-movement,

Mostly, the galvanometer gives full-scale deflection even when a few milliamperes current passes current passes through it. So for large current measurement, it should be modified.

Conservation of galvanometer into Ammeter

Shunt (bypass) resistor

A galvanometer can be converted into ammeter by connecting a low resistance Rs called shunt (bypass) resistor in parallel with the meter-movement (coil) of the galvanometer.

Range of Ammeter

Let, I be the range of ammeter.

Calculation of Shunt Resistance

Shunt resistance provides another path for the flow of current. The value of Rs is so adjusted that the current which gives full-scale deflection passes through the galvanometer and remaining current passes through the Rs.

Let

The resistance of galvanometer = Rg

Full scale deflection current = Ig

The current passing through Rs = I – Ig

Now, the potential difference across the Rg is,

Vg = Ig Rg  ————-  (1)

Similarly, the potential difference across the Rs is

Vs = Ig Rs

Vs = (I – Ig) Rs  ————  (2)

Since the galvanometer resistance Rg and the shunt resistance Rs are connected in parallel, so the potential difference between them must be same i.e.,

Vs = Vg

Putting values, we get

(I – Ig) Rs  = Ig Rg

Or

Rs  =  Ig Rg/ (I – Ig) —————-  (3)

The value of shunt Rs is very small. We can use a copper wire for this purpose which should be connected in parallel across the galvanometer. In order to increase the range of ammeter, Rs should be decreased.

What is voltmeter?voltmeter

The voltmeter is an electrical device which is used to measure the potential difference between two points. it is the modified form of the galvanometer. It is a high resistance galvanometer. It is always connected in parallel with the circuit component. An ideal voltmeter has infinite resistance.

Conservation of galvanometer into Voltmeter

High Resistance

A galvanometer can be converted into voltmeter by connecting a very high resistance Rh in series with meter-movement (coil) of the galvanometer.

Range of voltmeter

Let, the range of the voltmeter n= V (volts)

Calculation of High resistance (Rh)

The value of the high resistance Rh should be such that galvanometer gives full-scale deflection when it is connected to V volt.

Let,

The resistance of meter-movement = Rg

Full scale deflection current = Ig

Since Rg and Rh are in series, so

The combined resistance of the meter movement and Rh = Rg + Rh

Applying Ohm’s law, we have

V = Ig (Rg + Rh)

V = Ig Rg+ Ig Rh

Or           Ig Rh = V – Ig Rg

Or        Rh = V/Ig – Rg

This equation gives the value of the high resistance Rh which is used to convert the galvanometer into the voltmeter. The scale is calibrated from 0 to V to measure the voltage. In order to increase the range of the voltmeter, Rh should be increased.

The resistance of the voltmeter should be greater than the circuit resistance otherwise it will change the value of potential difference which is to be measured.

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