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Government Engineering 
College, Modasa 
Electrical Measurement And Measuring Instruments 
Module Name : Measurement Of Resistance 
Topic Name : Measurement Of Low Resistance 
Presented By: 
Kazim Marfatiya
Classification Of Electrical Resistance 
High resistance: under this category resistance is greater than 
0.1 M ohm. 
Medium resistance: under this category resistance is ranging 
from 1 ohm to 0.1M ohm. 
Low resistance: under this category resistance value is lower 
than 1 ohm.
Measurement of Low Resistance 
R<1Ω 
• The figure shows the construction 
of low resistance 
• For the protection of low 
resistance, it is constructed with 
four terminals 
 CC’ = Current Terminals 
 PP’ = Potential Terminals 
• The value of low resistance is 
measured between the potential 
terminal P and P’.
Method of Measurement of Low Resistance 
• Voltmeter and Ammeter Method 
• Kelvin Bridge Method 
• Kelvin’s Double Bridge Method 
• Recall our classification done above, as we move from top to 
bottom the value of resistance decreases hence, we require 
more accurate and precise device to measure the low value of 
resistance 
• We need some modification in Wheatstone bridge itself, and 
the modified bridge so obtained is Kelvin bridge, which is not 
only suitable for measuring low value of resistance but has 
wide range of applications in the industrial world
Voltmeter and Ammeter Method 
• There are two methods of connecting voltmeter 
and ammeter for measurement of resistance as 
shown in figure. 
• In both cases measured value of unknown 
resistance is equal to the reading of voltmeter 
divided by reading of ammeter. 
 From fig.(1) 
R = Rm ퟏ − 
푹풂 
푹풎 
 Ideally R = Rm only when Ra = 0 
 From fig.(2) 
 R = 
푹풎 
ퟏ− 
푹 
풎 
푹 
풗  Ideally R = Rm when resistance of voltmeter 
is ‘∞’
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)
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
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
Calculation Of Unknown Resistance by Kelvin’s Double Bridge 
• 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 = 풓 
풑+풒+풓 
푰 
So from eq.(1) I1P = IR + 풓 
풑+풒+풓 
푰 풑 ……….(5) 
I1Q = IS + 풓 
푰 풒 ………..(6) 
풑+풒+풓
Calculation Of Unknown Resistance by Kelvin’s Double Bridge 
• Divide eq. (5) & (6) 
• 퐼1푃 
퐼1푄 
= 
퐼푅+ 
푟푝 
푝+푞+푟 
퐼 
퐼푆+ 
푟푞 
푝+푞+푟 
퐼 
• Finally we get the below equation 
• R = 
푃 
푄 
푆 + 
푞푟 
푝+푞+푟 
푃 
푄 
− 
푝 
푞 
…….(7) 
• Usually, ratio 
푃 
푄 
is adjusted is equal to 
푝 
푞 
. So eq.(7) can be expressed as 
• R = 
푃 
푄 
푆 
• 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
Methods For Measuring Low resistance

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Methods For Measuring Low resistance

  • 1. Government Engineering College, Modasa Electrical Measurement And Measuring Instruments Module Name : Measurement Of Resistance Topic Name : Measurement Of Low Resistance Presented By: Kazim Marfatiya
  • 2. Classification Of Electrical Resistance High resistance: under this category resistance is greater than 0.1 M ohm. Medium resistance: under this category resistance is ranging from 1 ohm to 0.1M ohm. Low resistance: under this category resistance value is lower than 1 ohm.
  • 3. Measurement of Low Resistance R<1Ω • The figure shows the construction of low resistance • For the protection of low resistance, it is constructed with four terminals  CC’ = Current Terminals  PP’ = Potential Terminals • The value of low resistance is measured between the potential terminal P and P’.
  • 4. Method of Measurement of Low Resistance • Voltmeter and Ammeter Method • Kelvin Bridge Method • Kelvin’s Double Bridge Method • Recall our classification done above, as we move from top to bottom the value of resistance decreases hence, we require more accurate and precise device to measure the low value of resistance • We need some modification in Wheatstone bridge itself, and the modified bridge so obtained is Kelvin bridge, which is not only suitable for measuring low value of resistance but has wide range of applications in the industrial world
  • 5. Voltmeter and Ammeter Method • There are two methods of connecting voltmeter and ammeter for measurement of resistance as shown in figure. • In both cases measured value of unknown resistance is equal to the reading of voltmeter divided by reading of ammeter.  From fig.(1) R = Rm ퟏ − 푹풂 푹풎  Ideally R = Rm only when Ra = 0  From fig.(2)  R = 푹풎 ퟏ− 푹 풎 푹 풗  Ideally R = Rm when resistance of voltmeter is ‘∞’
  • 6. 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)
  • 7. 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
  • 8. 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
  • 9. Calculation Of Unknown Resistance by Kelvin’s Double Bridge • 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 = 풓 풑+풒+풓 푰 So from eq.(1) I1P = IR + 풓 풑+풒+풓 푰 풑 ……….(5) I1Q = IS + 풓 푰 풒 ………..(6) 풑+풒+풓
  • 10. Calculation Of Unknown Resistance by Kelvin’s Double Bridge • Divide eq. (5) & (6) • 퐼1푃 퐼1푄 = 퐼푅+ 푟푝 푝+푞+푟 퐼 퐼푆+ 푟푞 푝+푞+푟 퐼 • Finally we get the below equation • R = 푃 푄 푆 + 푞푟 푝+푞+푟 푃 푄 − 푝 푞 …….(7) • Usually, ratio 푃 푄 is adjusted is equal to 푝 푞 . So eq.(7) can be expressed as • R = 푃 푄 푆 • 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