SHUNT AND MULTIPLIER, RESISTIVITY AND CONDUCTIVITY

 

SHUNT AND MULTIPLIER, RESISTIVITY AND CONDUCTIVITY

SHUNT (Conversion of a Galvanometer to an Ammeter)

An ammeter is used for measuring currents. A galvanometer is used for detecting and measuring very small currents. We can convert the galvanometer into an ammeter by connecting a suitable resistor in parallel with the galvanometer. A resistor used for this purpose is known as a shunt. The shunt is a low resistance wire and is used to divert a large part of the current being measured but to allow only a small current to pass through the galvanometer.

Example

A galvanometer of internal resistance 100Ω gives a full scale deflection for a current of 10mA. Calculate the values of the resistance necessary to convert the galvanometer to an ammeter reading up to 10 A.

Solution

I = 10A

Current flowing through the shunt = 10 – 0.01 = 9.99A

P.d across shunt = (9.99 x R) V

P.d across galvanometer resistance = 0.01 x 100 = 1;  Since P.d across shunt = P.d across the galvanometer resistance

9.99R = 1; R= 1/9.99 = 0.10Ω

 

MULTIPLIER (Conversion of Galvanometer to a Voltmeter)

A galvanometer used for measuring very small currents can be converted to a voltmeter by connecting a high resistance or multiplier in series with the galvanometer.

Example

A galvanometer of internal resistance 100Ω gives a full scale deflection for a current of 10mA. Calculate the values of the resistance necessary to convert the galvanometer to an voltmeter reading up to 5 V.

Solution

rg = 100Ω, I = 10mA = 10 x 10-3A , R= ?, V= 5V

V = Multiplier + Galvanometer;  V = V1 + V2

V1 = 0.01 x 100 =1.0V;      V2 = I R;   5 = 1.0 + V2;   V2 = 5-1 =4V

R = V2 / I = 4.0V / 0.01A = 400Ω

RESISTIVITY

Resistivity is the resistance of unit length of material of unit cross-sectional area. The unit is ohm-metre (Ωm).

ꝭ = ; ꝭ- resistivity of the material, R- resistance, A- cross - sectional area , l- length

CONDUCTIVITY

Electrical conductivity (ẟ) is a measure of the extent to which a material will allow current to flow easily through it when a p.d is applied at a specified temperature. It is the reciprocal of the resistivity. Unit of conductivity is  (Ωm)-1.

ẟ =  

Example

Calculate the length of a Constantine wire of diameter 0.6 mm and resistivity 1.1 x 10-6 Ωm required to construct a standard resistor of resistance 35 Ω.

Solution

L= ?, d= 0.6mm, r = d/2 = 0.6/2 = 0.0003m, ꝭ=1.1 x 10-6 Ωm, R= 35Ω

A = ᴨr2 = 3.142 x (0.0003)2 = 9.0 x 10-8m2.

ꝭ = ;    l =  =  =  = 9m;  L=9m

Assignment

A galvanometer of resistance 50 Ω which gives a full-scale deflection for 1 mA, is to be adapted to measure currents of up to 5 A. (i) Calculate the resistance of the resistor required. (ii) If this resistor is made of a material of cross-sectional area  4x 10-4 cm2, and resistance  2.0 x 10-6 Ωcm. Calculate its length.

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