#### 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 Eab = Eint,

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 Rm = 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

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
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