1. What a Meter Bridge Is
A meter bridge is a simple device used to compare and determine unknown resistances. It works on the principle of the Wheatstone bridge but uses a uniform wire that is exactly one meter long—hence the name.
The wire is stretched tightly over a wooden board with a scale from 0 cm to 100 cm. By adjusting the position of a sliding contact, we find a point where the bridge circuit becomes balanced.
1.1. Purpose of the Meter Bridge
The meter bridge measures an unknown resistance by comparing it with a known, adjustable resistance. Instead of calculating directly, the device lets us find a balance point that makes the comparison accurate.
2. Principle Behind the Meter Bridge
The meter bridge works on the principle of a balanced Wheatstone bridge. When the bridge is balanced, no current flows through the galvanometer, and a ratio of resistances can be written using the lengths of the wire.
2.1. Condition for Balance
At the balance point, the ratio of the two resistances equals the ratio of the lengths of the wire on either side of the jockey:
\( \dfrac{R_X}{R} = \dfrac{L_1}{L_2} \)
Here:
- RX = unknown resistance
- R = known or standard resistance
- L1 = length from 0 to balance point
- L2 = length from balance point to 100 cm
2.1.1. Why Length Represents Resistance
The wire used in the meter bridge is uniform. This means resistance is directly proportional to length. Doubling the length doubles the resistance.
3. Working of the Meter Bridge
A galvanometer, a known resistance and the unknown resistance are connected so that the meter wire forms the fourth side of the Wheatstone bridge. Sliding the jockey along the wire changes the lengths on both sides and allows us to find the point of balance.
3.1. Steps in Finding the Balance Point
- Connect the known resistor and the unknown resistor in the two ratio arms.
- Press the jockey lightly at different points on the wire.
- Observe the galvanometer deflection.
- Move the jockey until the galvanometer shows zero deflection.
- Note the balancing length from the scale.
3.2. Using the Balance Point to Calculate Unknown Resistance
Once the balancing length L1 is found, the remaining length is L2 = 100 - L1. Substituting into the formula gives the unknown resistance.
\( R_X = R \dfrac{L_1}{L_2} \)
4. Important Notes While Using a Meter Bridge
For accurate measurements, the wire must be uniform and tightly stretched. Poor connections, loose jockey contact or dirt on the wire can affect the balance point. Reversing known and unknown resistors and taking an average reduces error.
5. Simple Visualisation
Think of the meter bridge like a balance scale. The jockey position acts like the point that balances both sides. Instead of weights, here the balance depends on electrical resistance and the lengths of a uniform wire.