# What is a Carey Foster Bridge & Its Working

In electronic circuits, a bridge circuit plays a key role in laboratory calculations to implement various electronic applications. Based on the design and construction of the bridge circuit, there are different types of bridge circuits like Wheatstone’s, Maxwell, Kelvin, Wein, Carey foster bridge, etc. To calculate resistance values Carey foster bridge circuit is used, invented by Carey foster in the year 1872. This article gives a detailed analysis of Carey foster bridge, circuit principle, and its working.

## What is Carey Foster Bridge?

The bridge circuit that can calculate medium resistances or can compare and measure the two large/equal resistance values with small variations is known as Carey foster bridge. It is the modified form of Wheatstone’s bridge circuit. It is also referred to as the method of small resistances.

### Carey Foster Bridge Principle

The Carey foster bridge principle is simple and similar to Wheatstone’s bridge working principle. It works on the principle of null detection. That means the ratios of the resistances will be equal and the galvanometer records zero where there is no current flow.

As we know, the bridge circuit is balanced when there is no current flow through the galvanometer. At an unbalanced condition, the current flows through the galvanometer and the reading is recorded by observing the deflection.

The **Carey foster bridge circuit diagram** is shown below. There are two units in the circuit

- Bridge Unit
- Testing Unit

The testing unit contains the power supply, galvanometer, and variable resistances which are to be measured. The DC supply is applied to eliminate the issues of battery discharge concerning time. So, it doesn’t show any impact on the output.

From the figure, the bridge circuit is constructed with P, Q, R, and S resistances. P and Q are the known resistances used for comparison. R and S are unknown resistances to be measured. The slide wire with a length L is placed between the resistances R and S as shown in the figure. To equalize/equivalent the ratios of resistances P/Q and R/S, the values of P and Q can be adjusted. Slide the contact of the slide wire to equivalent the resistance ratio.

Consider I1 be the distance from the left side where the bridge is balanced. Interchange the resistances R and S while the bridge gets balanced by sliding the contact with a distance of I2.

The switch is used to interchange the resistances R and S while testing. The galvanometer records zero when the bridge is balanced. The first bridge balance equation is,

**P/Q = (R+I1r) / [(S+(L+I1) r]**

Where r = resistance/unit length of the slide wire.

Now interchange the resistances R and S. Then the balanced equation for the bridge circuit is given as,

**P/Q = (S+I2r) / [(R+(L-I2) ]**

For the first balance equation, we get,

**P/Q + 1 = [(R+I1r+S+(L-I1) r] / [S + (L-I1)r] ……Eq (1)**

**P/Q= (R+S+I1r) / (S+(L-I1)r)**

We get a second bridge balance equation as

**P/Q + 1 = [(S+I2r+R+(L-I1) r] / [R + (L-I2)r] ….. Eq (2)**

**P/Q +1 = (S+R+Ir) / (R+(L-I2)r)**

From the above equations (1) and (2)

**S+(L-I1) r = R+(L-I1) r**

**S-R = (I1-I2)**

At the bridge balance condition, the difference between the resistances S and R is equal to the difference of distance between the lengths l1 and l2 of the slide wire.

Hence this type of bridge circuit is also called as Carey foster slide wire bridge circuit.

In practice, when the bridge is unbalanced, the galvanometer is connected in parallel with the low resistance, which avoids the burning of the circuit. The Carey foster bridge is sensitive where the measurement is to be done at the null point. and the known and unknown resistances are comparable.

#### Calibration of Slide Wire

To achieve the calibration of slide wire, place the resistances R or S in parallel with the known resistances of slide wire as shown in the figure.

For calibration of slide wire, consider S be the known resistance

S’ be the resistance value when connected in parallel.

**S-R = (I1-I2) r**

**S’-R = (I’1-I’2) r**

**(S-R) /(I1-I2) = (S’-R) /(I’1-I’2)**

To get the value of R to solve the above equation,

**R = [S(I’1-i’2) – S(I1-I2)] / [(I’1-I’2-I1+I2)] … .. Eq (3)**

By using Carey foster bridge, the values of resistances R and S can be compared and measured directly concerning length. The resistances P, Q, and slide contact are eliminated.

**Errors while Constructing Carey Bridge Circuit and Calibrating Slide Wire**

The constant resistance is excessive when the edges of the connected wires, copper strips, and resistance end tips are not clean.

Tight connection of fractional resistances can develop adverse resistance contact when the current flows through the slide wire for a longer period, then the wire may get heated up and get damaged.

While sliding the length of the wire, it might be non-uniform and the cross-sectional dimension of the wire can be modified.

### Advantages

The **advantages of Carey foster bridge** are

- The complexity of the bridge circuit is reduced because there is no need for additional equipment except the slide wire and the resistances.
- It can be utilized as the meter bridge where the slide wire length can be increased by connecting resistances in series. Hence the accuracy of the bridge circuit is increased.
- Construction is simple and easy to design
- The components used in the circuit are not complex

### Applications of Carey Foster Bridge

The applications of Carey foster bridge are as follows

- It is used to calculate the values of medium resistances
- It is used to compare the approximate values of equal resistances
- It is used to measure the value of the specific resistance of the slide wire. > Used in light detector circuits.
- Used to measure the intensity of light, pressure, or strain. Since it is a modified form of Wheatstone’s bridge

Thus, this is all about an overview of Carey foster bridge circuit- definition, principle, circuit, advantages, applications, and calibration of slide wire. Here is a question for you “What are the disadvantages of Carey foster bridge? “