Measurement of Low resistance - Engineering Notes

Low Resistance:

• Resistances of about 1ohm and less are included in this class.
• Measurement of low resistances are required for determination of resistances of armatures and series field windings of large machines, ammeter shunts, cable length, contacts etc.

Measurement of Low Resistance:

1. Four wires are used for representation of low resistance.
2. This can be measured by 

• Ammeter - voltmeter method
• Kelvin's double bridge method
• Potentiometer method

1. Ammeter Voltmeter Method:

Voltmeter - Ammeter method:

Voltmeter - Ammeter method for measurement of medium resistance

Measured value of resistance, Rml = (VR + Va ) / IR

where R is the true value of the resistance.

Error = Ra% = Ra / R

• In this method, always the measured value of resistance is greater than true value of resistance.
• This  method is suitable for measurement of high resistance, among the range.

Ammeter - voltmeter Method:

Ammeter - Voltmeter method for measurement of medium resistance

Measured value of resistance, Rm2 = VR / I

where I = IR = IV = (VR / R1) +( VR / Rv)

then Rm2 = R / ( 1 +( R / Rv))

Error  = Rm2 - R = Rm2

% error = -Rm2 / Rv = -R / Rv

• In this method, always the measured value of resistance is less than true value of resistance.
• This  method is suitable for measurement of low resistance, among the range.

The resistance where both the methods give same error is obtained by equating the two errors.

Ra / R = R / Rv

R = sq root (Ra.Rv)

2. Kelvin's double bridge method: 

 It is modification of the wheatstone bridge  and provides increased accuracy. It incorporates the idea of second set of ratio arms, hence the name double bridge and the use of four terminal resistances for the low resistance arms. The circuit diagram is shown in the figure.

P, Q and p ,q are two pairs of known non - inductive resistances and one pair P , p or Q, q is variable. the ratio p /q is made equal to P /Q.
Where R = unknown resistance
S = Standard resistance of the order of magnitude as R
r = Connecting link of low resistance

Schematic diagram of Kelvin's double bridge method

Vad = Vam + Vmd = I2.R + I2. r . P/ (p+q+r)

R = S . P. q.r .[ P/Q - p/q]  /  Q. (p+q+r)

3. Potentiometer Method:

It is based on comparison of one resistance against another. The unknown resistance R, an ammeter A and a variable resistance for limiting current and a standard resistance S are connected in series with a low voltage, high current supply. The current flowing through the circuit is adjusted so that the potential difference across each of the resistor is about 1v. The voltage drop across both the unknown resistor R and standard resistor S are measured by a d.c potentiometer.