how to measurement low resistance

1. Gandhinagar institute of
technology
• Sub –Electrical Measurements and measuring
Instruments
• Topic – Measurement of low resistances
• Guided by – Prof. Rahil Parikh
• Sem – 3rd
• Branch – Electrical (b3)
• Academic year – 2015&2016

2. Prepared By:-
• Sodha Manthansinh (140120109057)

3. Introduction
• The measurement of resistances is as
important as the measurement of any other
electrical parameter.
• The basic knowledge of resistance
measurement is necessary to understand the
working of the other instruments used for the
measurement of other electrical quantities.

4. Classification of resistances
• (1) Low Resistances
• (2) Medium Resistances
• (3) High Resistances

5. Different methods used for
measurement of Low Resistances
• (1) Voltagemeter-Ammeter Method
• (2) Kelvin Double Method
• (3) Potentiometer Method

6. (1) Voltmeter-Ammeter Method
• Rx = Resistance value to be measured
• V = Voltmeter reading
• I = Ammeter reading

7. • The two types of connections are used in this
method. The connections are shown in the fig
(a) and (b).

9. Kelvin Bridge
Ry = represents resistance of connecting
lead from R3 to Rx.
Connection
of G
• To point ‘m’
• To point ‘n’
Value of Rx
• Higher than
the actual
• Lower than
the actual
Figure (2)

10. Calculation Of Unknown Resistance by Kelvin Bridge
• From Fig.(2)
Rnp
Rmp
= R1
R2
• The balance condition of bridge is
Rx +Rnp =
R1
R2
(R3 + Rmp)
• Substituting from eq.(1)
Rx +
R1
R2
Rmp =
R1
R2
R3 +
R1
R2
Rmp
Rx =
R1 R3
R2
 The problems with the above method are :-
• the method is not practical
• difficult to find correct galvanometer null point

11. Kelvin’s Double Bridge Method
To Overcome the problem Of Kelvin Bridge ,
The New Bridge is Introduced ,which is used for
precise measurement of low resistance called
Kelvin’s Double Bridge.
 Construction
• Consist of 2 ratio arms
• Connected resistances are P, Q,
p,q,r,S,R.
• r is the resistance of slide wire
• R is the unknown resistance
• Rg is regulating resistance
• Galvanometer (G) is connected
between point ‘F’ and ‘H’.
 Working
• By adjusting the balanced
condition, we can find the
unknown resistance

12. • At Balance condition Ig = 0.
• Hence voltage across ‘P’ = voltage across ‘R’ + voltage across ‘p’
VP = VR + Vp
I1P = IR + I2p ……(3)
• Similarly voltage across ‘Q’ = Voltage across ‘S’ + voltage across ‘q’
VQ = VS + Vq
I1Q = IS + I2q …….(4)
• Voltage across ‘r’ = voltage across (p+q)
Vr = V(p+q)
So,
I2 = 𝒓
𝒑+𝒒+𝒓
𝑰
So from eq.(1) I1P = IR + 𝒓
𝒑+𝒒+𝒓
𝑰 𝒑 ……….(5)
I1Q = IS + 𝒓
𝒑+𝒒+𝒓
𝑰 𝒒 ………..(6)
Calculation Of Unknown Resistance by Kelvin’s Double Bridge

13. • Divide eq. (5) & (6)
• 𝐼1𝑃
𝐼1𝑄
=
𝐼𝑅+
𝑟𝑝
𝑝+𝑞+𝑟
𝐼
𝐼𝑆+
𝑟𝑞
𝑝+𝑞+𝑟
𝐼
• Finally we get the below equation
• R =
𝑃
𝑄
𝑆 +
𝑞𝑟
𝑝+𝑞+𝑟
𝑃
𝑄
−
𝑝
𝑞
…….(7)
• Usually, ratio
𝑃
𝑄
is adjusted is equal to
𝑝
𝑞
. So eq.(7) can be expressed as
• R =
𝑃
𝑄
𝑆
• For accurate measurement of ‘R’ two readings are taken by reversing the direction of current,
the average value of these two values is taken as magnitude of unknown resistance
Calculation Of Unknown Resistance by Kelvin’s Double Bridge