**Objective:**

To measure low unknown resistance using kelvin’s double bridge.

**Theory:**

The double bridge is a modified version of the whinstone bridge. And understanding the kelvin double bridge arrangement may be obtained by a study of the differences that arise in a Wheatstone bridge on account of the resistance of the leads and the contact resistance while measuring low valued resistors.

The kelvin double bridge method is a popular method of calculating an unknown resistance using bridge circuit where resistors above about 1 ohm in value can be measured with great accuracy.

The kelvin double bridge gives the idea of second set of a second set of ratio-arms, hence the name double bridge and the use of four terminal resistors for low resistance arms.

The Kelvin Double bridge is a popular method of calculating an unknown resistance using a bridge circuit where resistor above about 1 ohm in value can be measured with great accuracy.

The bridge consists of four arms with three standard resistances and one unknown resistance and operates upon a null indication principle.

This means the indication is independent of the calibration of the null indicating instrument or any of its characteristics. For this reason, very high degree of accuracy can be achieved using Wheatstone bridge. Accuracy of 0.1 % is quite common with a Wheatstone bridge as compared to accuracies of 3 % to 5 % with ordinary ohmmeter for measurement of medium resistance.

Fig, shows basic circuit of a Wheatstone bridge. It has four resistance P,Q,R & S together with a source of emf (a battery) and a null detector.

**Circuit Diagram:**

The current through the galvanometer depends on the potential difference between points c & d, the bridge is said to be balanced when there is no current through the galvanometer or when potential difference across the galvanometer is zero. This occurs when the voltage from the point ‘c’ to ‘a’ equals the voltage from point ‘d’ to point ‘a’; or, by referring to the other battery terminal, when the voltage from point ‘c’ to point ‘b’ equals the voltage from point ‘d’ to point ‘b’.

Therefore,

I_{1}P=I_{2}R

`QR=PS`

This is the balanced equation of Wheatstone bridge.

If three of the resistance are known then the fourth unknown resistance can be expressed in the form:

S is called the standard arm and P and Q are called the **ratio arms**.

Now,

For measurement of low resistance values less than 1Ω, the resistance of leads and contacts, though small, are appreciable in comparison in the case of low resistance. Hence special techniques like the Kelvin’s Double bridge are used to measure these low resistances with minimum error.

The order of the resistance values varies from 0.1µΩ to 1Ω.

The operations of the Kelvin Bridge is very similar to the Wheatstone bridge.

The Kelvin Double Bridge incorporates the idea of a second set of ratio arms- hence the name: double- bridge-and the use of four terminal resistors for the low resistance arms. Let the first ratio arms be P and Q. Let the second ratio arms e p and q and let p and q used to connect the galvanometer to a point ‘d’ at the appropriate potential between points (say m and n) to eliminate the effect of connecting lead resistance r between the unknown resistance R and the standard resistance S.

The ratio p/q is made equal to P/Q. Under balance conditions there is no current through the galvanometer which means that the voltage drop between a and b, E_{ab} is equal to voltage drops E_{amd }between a and d.

Circuit Diagram for experimental set-up:

Equation (2) is the usual working for the Kelvin Bridge. It indicates that the resistance of connecting lead, r, has no effect on the measurement, provided that the two sets of ratio arms have equal rations.

**Procedure:**

- Identify the current terminals (C1 and C2) and potential terminal (P1 and P2) on the portable kelvin Double Bridge kit and connect to the corresponding current and potential terminals of the unknown resistance box (which is measurable).
- Connect the kit to the AC power supply

.

- Calculate the resistance using the formula (a×b+c), for every reading.
- Tabulates the readings.

**Calculation:**

**Conclusion**