Measurement of Low, Medium and High Resistance

Resistance measurement

1: Classification of resistance

• Low resistance is the range of 0.1ohm to 1 ohm.
• Medium resistance is the range of 1 ohm to low mega ohm.
• High resistance is 0.1 megaohm to a higher range.

2: Methods for the measurement of low resistance

• Kelvin double bridge
• Ammeter – voltmeter method

3: Methods for the measurement of medium resistance

• Ammeter – voltmeter method
• Wheat stone bridge method
• Ohm meter method

4: Methods for the measurement of high resistance

• Direct deflection methods
• Loss of charge methods
• Megha ohm bridge method

Kelvin double bridge for measurement of low resistance

Kelvin bridge, a modification of wheatstone bridge, method increases the accuracy in measurement of low resistance
and remove the effects of connecting leads and contact resistance. Here, r represents the resistance of connecting leads that connects the unknown resistance R and standard resistance S.

The galvanometer is connected at point d that divides the resistance r into r₁ and r₂ such that,

$$\frac{r_{1}}{r{_{2}}} = \frac{P}{Q}$$

using equation we have,

$$ \Rightarrow \frac{r_{1}}{r_{1}+r_{2}} = \frac{P}{P+Q} \Rightarrow r_{1} = \frac{P}{P+Q} r $$

$$ \Rightarrow \frac{r_{1}+r_{2}}{r_{2}} = \frac{P+Q}{Q} \Rightarrow r_{2} = \frac{Q}{P+Q} r $$

from the figure at balance condition

$$\frac{R+r_{1}}{S+r_{2}}=\frac{P}{Q}$$

$$R+r_{1}= \frac{P}{Q} (S+r_{2})$$

$$R+\frac{p}{P+Q}r = \frac{P}{Q}(S+\frac{Q}{P+Q}r)$$

$$R=\frac{P}{Q}S$$

So, connecting the galvanometer at point d, the resistance of leads does not effect the result , but the problem with the above method are

• the method is not practical
• difficult to find correct galvanometer null point.
  
  

To solve the above problems, two actual resistance unit of correct ratio is connected between points m and n as shown in figure which is original kelvin double bridge, the ratio arm of p and q is connected at d to eliminate the effect of connection.

Under balance condition there is no current through Galvanometer, Thich means E_ab = E_int,

_where,

This equation shows that the resistance of connecting leads has no effects but error may be introduced in the ratio arms , ie. p/q = P/Q may not be equal. thermoelectric effect can be removed by reversing the battery connection and true value of R will be the mean of two readings.

In AV method the mesured resistance is given by R_m = V/I, where v and I is the voltage and current reading of voltmeter and ammeter respectively. The available connection methods are shown in figure.

AV measure to measure medium resistance

If test resistance is greater than that of calculated from equation (1.10) then figure (1.1) (a) is used, otherwise figure (1.1) (b).

Loss of charge methods for the measurement of high resistance

In this method the insulation resistance R to be measured is connected in parallel with a capacitor C and a electrostatic voltmeter. The capacitor is charged to some suitable voltage by means of supply voltage V and then allowed to discharge through the resistance.

The voltage across the capacity v at any instant t after application of supply voltage v as shown in figure is given by

V= Ve^-t/RC

Therefore, the insulation resistance,

More accurate result may be obtained by using change in voltage V=v directly and callinf this change e, ie.

This method is suitable for high resistance measurement but it requires a capaciter having very high leakage resistance as high as the resistance being measured. This method is also time consuming.

Actually in this method the effect of the resistance of electrostatics voltmeter is ignored and the leakage resistance of the capacitor is assumed infinite. in practical, correction must be applied. In below figure ,R₁ represents the resistance of voltmeter and capacitor.

The measured resistances,

Where

R' represents the resistance when two resistance are in operation, test is repeated disconnecting the resistance R, Then the true value R is obtained by using the above equation.

References-

1.Stevens, S.S. (1946)On the theory of scales and measurement. Science.

2.S.morris.alan(2001). Measurement and Instrument principle(3 ed.).A division of Reed Educational and Professional Publishing Ltd