# Electrical Shunt

Galvanometer is very sensitive device. Flow of huge amount current can burn galvanometer or displaces spring of it. For saving galvanometer a small value parallel resistor is connected across it and makes another way out of flowing current. Parallelly connected resistor is called shunt. Total current divides into two ways. Maximum current flows through shunt resistor due to low resistance and small amount of current flow. In this way shunt saves galvanometer from damage.

Parallel connection of small value resistor across galvanometer which saves galvanometer from damage of huge current flow is called shunt.

**Relation between galvanometer current and shunt current with total current**

**Figure:** Galvanometer Shunt

Suppose Galvanometer resistance G. A shunt resistor S is connected parallelly with galvanometer at A and B points. Total current I comes across A point and divides into two paths I_{g} through galvanometer and I_{s} current shunt resistor.

Total current, I = I_{g} + I_{s}

Potential of A and B point are V_{A} & V_{B}.

According to Ohm’s law for galvanometer, V_{A} – V_{B} = I_{g}G

For shunt, V_{A} – V_{B} = I_{s}S

From two above equation, I_{s}S = I_{g}G

Or I_{s }/ I_{g} = G/S

Adding by 1 both sides we get,

If we multiply galvanometer current with (G+S)/S then we get total current. So (G+S)/S is called shunt factor.

If a shunt is connected across galvanometer parallelly and the factor multiplication with galvanometer current results to total current is called shunt factor.

**Ammeter range extension **

**Ammeter Shunt**

The device which measures the current flow in ampere unit is known as ammeter.

The resistance of ammeter is very low. For measuring of current ammeter is connected in series. An ammeter range is the capability of it current measurement. A low current measuring ammeter can be upgrading into high current measurement ammeter. That means a low range ammeter can be converted into high range ammeter. For that a low resistance is connected as shunt across ammeter parallelly. Low resistance is used cause maximum current passes through the shunt resistance. In this way n times excess current can be measured using shunt resistance.

Suppose internal resistance of ammeter is r, it can carry maximum I current. For measuring nI current from ammeter S resistor is connected parallelly.

**Figure:** Ammeter Shunt

Here G = r

I = nI

Or nS = r + S

Or (n-1) S = r

For measuring n times extra current r/ (n-1) resistance can be connected in parallel.

**Example: Internal resistance of an ammeter 1.8****Ω****. It can measure 1A current. For measuring 10A current how a shunt should be connected?**

**Answer: **

Given,

Internal resistance of ammeter, r = 1.8Ω

n = I′/I=10/1 = 10

We know,

0.2Ω shunt resistance should be connected in parrallelly across ammeter.

**Voltmeter range extension **

**Voltmeter Shunt**

The device which can measure the voltage of two points in any circuit in volt unit called voltmeter.

For measurement of voltage of any two points voltmeter should be connected in parallel with it. Normally internal resistance of a voltmeter is greater than ammeter internal resistance.

The capability of measuring maximum voltage for a voltmeter is called range of the voltmeter. A low range voltmeter can be extended up to high range voltmeter easily. In other words a low voltage range measuring voltmeter can be capable of measurement high range voltage. The capacity measurement voltage of any voltmeter can be extended n times more as its normal range.

To do so a high value resistance should be connected in series with voltmeter which is called multiplier.

**Figure:** Voltmeter Shunt

Let,

Internal resistance of a voltmeter r,

It can take I_{g} current through it

and it can measure maximum V voltage.

For measuring *nV* amount of voltage *R* quantity resistance should be connected in series with the voltmeter.

So, R = (n-1) × voltmeter internal resistance

From this equation it is clear for measuring n times voltage (n-1) time value of internal resistance of voltmeter should be connected in series across it.

**Example: A voltmeter can measure maximum 15V and it’s internal resistance 1000****Ω****. For measuring 150V from the voltmeter what step should be taken?**

**Answer:**

Here,

Internal resistance of voltmeter, r = 1000Ω

Maximum capacity of voltage measurement of voltmeter, V = 15V

Expected capacity of voltage measurement of voltmeter, V^{′} = 150V

Essential resistance connection in series, R = ?

But n = V^{′}/V = 150/15 = 10

We know,

R = (n-1) × r

= (10 – 1) × 1000

R = 9000Ω

For measuring 150V voltage 9000Ω should be connected in series with voltmeter.

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