## What is a Kelvin Double Bridge and Its Working

- Frank
- May 25, 2022
- read:

A bridge is an electrical circuit that consists of three branches that are connected at a common point and the intermediate bridging which is present can be adjustable. They are mainly used in an electrical Laboratory for measuring various parameters and in application like filtering, linear and nonlinear, etc. Bridges are classified into two types they are, DC bridges like Wheatstone Bridge, Kelvin Double Bridge, Mega Ohm Bridge and AC bridges like Inductance, Capacitance, Frequency. For measuring a small value of resistance like 1 ohm, we can either use an ohmmeter or a Wheatstone bridge, but in a case where the resistance value is less than 1 ohm, it will be difficult to measure. Hence, we shunt a lower value of the unknown resistors, 2 precision resistors, and a high current ammeter to form four-terminal resistors, where the current flows through the circuit, then the voltage drop across the resistors can be measured using a galvanometer, which together is a four-terminal resistor called kelvin bridge.

### What is Kelvin Double Bridge?

**Definition:** A kelvin bridge or kelvin double bridge is a modified version of the Wheatstone bridge, which can measure resistance values in the range between 1 to 0.00001 ohms with high accuracy. It is named because it uses another set of ratio arms and a galvanometer to measure the unknown resistance value. The basic operation of the Kelvin double bridge can be understood from the basic construction and operation of the kelvin bridge.

### Principle of Kelvin Bridge

A Wheatstone bridge is used to measure resistance equal to or greater than 1 – ohm, but if we want to measure the resistance below 1 – ohm, it becomes difficult because the leads which are connected to the galvanometer adds up the resistance of the device along with the resistance of leads leading to variation in the measurement of the actual value of resistance. Hence in order to overcome this problem, we can use a modified bridge called kelvin bridge.

### Derivation for Finding Unknown Resistance Value

The Kelvin bridge is of resistance “r” which connects “R” ( unknown resistor ) to standard resistor “S”. The resistance value can be viewed in the galvanometer (from “m to n”). If the pointer in the galvanometer shows at “m”. It means, the resistance value is less and if the pointer shows at “n” means the resistance value is high. Hence rather by connecting galvanometer to “ m and n “ we choose another intermediate point “d” in kelvin bridge as shown in figure

The value of resistance can be calculated as follows

**r1 / r2 = P/Q …………(1)**

**R + r1 = (P/Q) * (S+r2)**

Where from 1

**r 1 / ( r1+ r2) = P / (P+Q)**

**r1 = [P / (P+Q) ].r**

we know that **r1+r2 =r**

**r2 = [Q / (P+Q)] .r**

**R +[ P/( P + Q)] * r = P/Q [ S+ (Q/(P+Q)*r)]**

**R = (P/Q)*S ………….(2)**

From the above equation, we can say that by connecting the galvanometer at point “d” there will be no effect in the measurement of the actual resistance value, but the only disadvantage of this process is that it is difficult to implement, hence we use a Kelvin double bridge for getting accurate low resistance value.

### Circuit Diagram of Kelvin Double Bridge

The construction of Kelvin double bridge is similar to the wheat stone bridge, but the only difference is it consists of 2 arms “P & Q”, “p & q” where the arm “p & q” is connected to one end of the galvanometer, at “d” and “P & Q” is connected to another end of the galvanometer, at ‘b’. This connection minimizes the effect of connecting lead and the unknown resistor R & a standard resistor S is placed between ” m and n”, and “a and c”.

### Derivation

The ratio p/q = P/Q,

Under the balanced condition current in galvanometer = 0

Potential difference at a & b = voltage drop between Eamd .

**Eab = [P / P+Q ] Eac**

**Eac = I [ R + S + [( p+q)r] / [p+q+r]] …………(3)**

**Eamd = I [ R + (p / (p+q)) * {(p+q) r / (p+q+r)}]**

**Eac = I [ p r / ( p+q+r)] ………(4)**

When galvanometer shows zero then

(**P / P+Q) * I [ R + (p / (p+q)) * {(p+q) r / (p+q+r)} ] = I [ p r / (p+q+r)]**

**R = (P /R)* S + p r / (p+q+r) [ (P/Q) – (p/q)]**

We know that **P/Q = p/q**

**R = (P/Q) * S …….(5)**

For obtaining perfect results, the arms ratio should be maintained equal and the thermo-electric electromagnetic field induced in the bridge while taking readings can be reduced by interchanging the polarity of the connection. Therefore the unknown resistance value can be obtained from the two arms. Typically, it measures 1 – 0.00001 ohm with an accuracy ± 0.05% to ±0.2%, in order to achieve sensitivity the current to be supplied should be large.

### Advantages

The advantages are

- It can measure the resistance value in the range of 0.1 µA to 1.0 A.
- Power consumption is less
- Simple in construction
- Sensitivity is high.

### Disadvantages

The disadvantages are

- For knowing whether the bridge is balanced or no, the sensitive galvanometer is used.
- To obtain good sensitivity of the device, a high current is required.
- Manual adjustments are to made periodically when required.

### Applications

The application of the Kelvin double bridge is

- It is used to measure the unknown resistance of a wire.

### FAQs

**1). What are the different types of bridges?**

Bridges are usually classified into two types they are, DC bridge (Wheatstone Bridge, Kelvin Double Bridge, Mega Ohm Bridge) and AC bridge (Inductance, Capacitance, Frequency).

**2). Why is the Kelvin double bridge used?**

Kelvin double bridge is a modified form of Wheatstone bridge, which is used to measure lower resistance values in the range of 1 to 0.00001 ohms.

**3). Why is Kelvin double bridge used to measure low resistance?**

While measuring low resistance value the contact and lead resistance cause significant error in reading, hence in order to overcome this error kelvin double bridge is used.

**4). What is the difference between the Wheatstone and Kelvin Double Bridge?**

Wheatstone bridge measures the resistance greater than or equal to 1 – ohm by balancing the circuit, whereas Kelvin double bridge is modified form of Wheatstone, which is used to measure lower resistance values in the range of 1 to 0.00001 ohms.

**5). When the bridge is balanced, how much current flows through the galvanometer?**

‘0’ zero current flows through the bridge when the bridge is balanced.

**6). What is the effect of load and contact resistance in kelvin bridge?**

There is no effect of load and contact resistance in the Kelvin bridge since the bridge is independent of load and contact resistance.

**7). What is the accuracy of Kelvin Double Bridge?**

The unknown resistance value can be obtained from the two arms of Kelvin double bridge, typically, it measures 1- 0.00001 ohm with an accuracy ± 0.05% to ±0.2%.

A bridge is an electrical circuit, which is used in Labourites for measuring various parameters. They are usually classified into two types they are, DC (Wheatstone Bridge, Kelvin Double Bridge, Mega Ohm Bridge) and AC bridges (Inductance, Capacitance, Frequency). This article gives an overview of the Kelvin double bridge, a kelvin bridge or kelvin double bridge is a modified version of Wheatstone bridge, which can measure resistance values in the range between 1 to 0.00001 ohm’s with an accuracy ± 0.05% to ±0.2%. The main advantage of this bridge is that it can measure even small resistance value.