What is the principle of Carey bridge?

Carey bridge is used to determine an unknown resistance by balancing it against a known resistance using a Wheatstone bridge arrangement. The principle of Carey bridge mainly lies in the concept of Wheatstone bridge balance, where the potential difference between two points in the bridge circuit becomes zero.

Carey Bridge Principle:

Consider the Carey bridge circuit shown below:

[Image of Carey bridge circuit with labels]

In the Carey bridge circuit:

- R: Unknown resistance

- S: Standard known resistance

- P, Q: Ratio arms

- G: Galvanometer

- B: Battery

When the bridge is balanced, the galvanometer (G) shows no deflection, indicating that there is no potential difference between points C and D. At this balance condition, the following equation holds:

```

R/P = S/Q

```

Rearranging the equation to solve for the unknown resistance (R):

```

R = (S/Q) * P

```

Now, the ratio of the arms P and Q is determined using a jockey and contact slider that moves along the bridge wire. The slide makes contact with the bridge wire at a point (C) where the bridge becomes balanced and the galvanometer reading becomes zero. The lengths AC and CD on the bridge wire are measured, and the ratio P/Q is calculated as the ratio of these lengths.

```

P/Q = AC/CD

```

By substituting the ratio of the bridge wire arms (P/Q) back into the equation for R, we get:

```

R = (S/Q) * P = (S * AC)/CD

```

Therefore, the unknown resistance (R) can be determined by measuring the lengths AC and CD on the bridge wire, known resistance (S), and using the Carey bridge principle.