# Measuring Low Resistance Using Kelvin Double Bridge

We aim to measure the resistance of a given resistor using Kelvin Double Bridge and determine its tolerance. Kelvin Double Bridge is nothing but a modification of Wheatstone bridge. It is used for measuring of low resistance to a good precision. It compares two ratio arms P,Q and p,q and hence is called ‘double bridge’.

P, Q, p, q are the resistances in the ratio arms. G is a galvanometer of D’Arsonal type, used as a null detector. S is a small standard resistor, R is a resistance under measurement. Usually low resistance consists of four leads. Two of them are called as voltage leads and remaining as current leads. “r” is the resistance of connecting lead between R and S.

Under balanced conditions,

From the above equation, it is clear that the resistance of connecting leads “r” has no effect on the measurement if the two sets of ratio arms have equal ratios ie, P/Q = p/q.

The effect of thermo-electric Emf can be eliminated by making other measurement with battery terminals reversed and taking the average of the two readings can eliminate the effect of thermo-electric emfs.

### Procedure for the measurement of low resistance R using Kelvin Double Bridge

1. Move the Galvanometer switch to increase position. This connects the built-in galvanometer to the circuit. If an external more sensitive galvanometer is available, connect it to the terminals marked “extgalv” and put the galvanometer switch in “EXT” position.
2. Four terminals are provided for connecting unknown resistance of the bridge circuit. They are labeled by “+C, +P, -C, -P”. Here +C and -C constitute the current terminals. If the given unknown resistance is of four leads then connect the two potential leads to +P & -P and current leads to +C & -C with correct current polarity. If the unknown resistance has two terminals then the leads from +C and +P are connected to other terminals of unknown resistance.
3. Now, press the button on the panel and obtain the balance by varying the dials.
4. Under balanced conditions, the sum of two dials multiplied by multiplier sitting gives the value of unknown resistance.
5. Find the tolerance of the resistance and tabulate the results. The example results are as given in the tabular form below:

 S.No For Kelvin Double Bridge Calculated Value From Multimeter Theoretical Value(Ω) % Tolerance 1. [1 + 0.001×0] x 100 = 100 100.2 0.199 2. [0 + 96 x 0.001] x 100 = 9.6 10.7 10.2 3 [0.9 + 49 x 0.001] x 100 = 94.9 95.4 0.52

### Precautions

• Press the push button immediately during the course of balance.
• A variable high resistance should be connected in series with galvanometer for initial adjustments in order to protect it from high currents. Once the balance point is reached, the resistance should be cut-off to increase the sensitivity.