Find Resistance using Meter Bridge

Aim

To find resistance of a given standard resistor using metre bridge.

Apparatus and Material Required

• Metre bridge,
• Standard resistor,
• A resistance box,
• Galvanometer,
• A jockey,
• One-way key,
• DC Power supply (battery eliminator),
• Thick connecting wires,
• Rheostat (for adjusting current),
• A piece of sandpaper

Description of the Apparatus

Meter Bridge
Meter bridge consists of one-meter-long constantan wire with uniform cross-sectional area and three thick metal strips, two bent at ninety-degree angles. Mounted on a wooden board marked with a scale, these components create a setup that provides precise measurements. There is a galvanometer that work as bridge for the parallel branches in the circuit. The accompanying diagram shows the setup and the connections.

Resistance of the wire AB per unit length is \(r\). Thus, the resistance of the wire of length \(l\) is given by \(r\times l\).

There are two gaps \(E\) and \(F\) in which resistors are connected. The terminal, \(C\) between these gaps is connected with a jockey , \(J\) through a galvanometer. The jockey slides over the wire to locate the point where the Wheatstone bridge is balanced.

Principle

The meter bridge works on the principle of Wheatstone bridge. It states that if there is no current flowing in the bridge wire connecting the two branches of a parallel circuit then the ratio of resistances in two branches of the circuit is equal.
This is the balanced condition of Wheatstone bridge.

In the accompanying diagram, there are two branches of the Wheatstone bridge. One contains two resistors \(R_{1}\) and \(R_{2}\) in series while another contains two resistors \(R_{3}\) and \(R_{4}\) again in series.

As there is no current through the galvanometer, i.e. \(I_{g} =0\), \[\dfrac{R_{1}}{R_{2}}=\dfrac{R_{3}}{R_{4}}\],

In the meter bridge, \(R_{x}\) is the wire resistor whose resistance is to be found. \(R_{box}\) is known resistance (resistance box). The wire segments \(AD\) and \(DB\) has the resistances \(R_{AD}\) and \(R_{DB}\) respectively. Their values are \[R_{AD}= r\times l\] \[and\] \[R_{DB}= r\times (100-l)\]

Thus, \[\dfrac{R_{x}}{R_{box}}=\dfrac{R_{AD}}{R_{DB}}\]

\[\dfrac{R_{x}}{R_{box}}=\dfrac{r\times l}{r\times (100-l)}\]

\[\dfrac{R_{x}}{R_{box}}=\dfrac{l}{(100-l)}\]

\[R_{x} = R_{box} \times \dfrac{l}{(100-l)}\]

Thus, knowing \(l\) and \(R_{box}\), we can find \(R_x\).

Procedure

1. Set up:
   • Clean the ends of the connecting wires with the help of sandpaper in order to remove any insulating coating on them.
   • Make connections to set up the circuit as shown in the meter bridge diagram. Connect unknown resistor in gap E and the resistance box \(R_{box}\) in gap F.
2. Find null points
   1. Introduce some resistance R in the circuit from the resistance box. Bring the jockey J in contact with terminal A first and then with terminal B. Note the direction in which pointer of the galvanometer gets deflected in each case. Make sure that jockey remains in contact with the wire for a fraction of a second. If the galvanometer shows deflection on both sides of its zero mark for these two points of contact of the jockey, null point will be somewhere on the wire AB.
   2. If it is not so, adjust resistance R so that the null point is somewhere in the middle of the wire AB.
   3. Interchange the position of the resistances \(R_x\) and \(R_{box}\). The interchange takes care of unaccounted resistance offered by terminals.
   4. Repeat the steps 1,2, and 3, three more times with different resistances from resistance box.

Observations

Calculations

Average resistance = \(\frac{19.5+19.9+19.9+20.1+20.4}{5} = 20.0 \Omega \).

Results

Resistance of the given resistor is \(20.0 \Omega \).

Precautions

1. All the connections and plugs should be tight.
2. Jockey should be moved gently over the metre bridge wire.
3. Only insert the key while taking observations to avoid the heating of the wire, which can impact its resistivity.
4. Null points should be in the middle of the wire (30 cm to 70 cm).

Sources of error

1. Effect of end resistances due to copper strips, connecting screws, may affect the measurement.
2. The resistances of end pieces/metal strips may not be negligible. The error introduced by it can be reduced by interchanging the known and unknown resistances in gaps E and F.
3. Galvanometer pointer is expected to be at zero when no current flows through it. However, many times it is observed that it is not so. In such cases, pointer has to be adjusted to zero by gently moving the screw below the scale with the help of a screw driver. Otherwise null point must be obtained by tapping the jockey on the wire.

Conclusion

In this experiment, the resistance of the given standard resistor was successfully determined using the meter bridge. The experiment validates that the meter bridge is a reliable and precise instrument for determining resistance, provided careful attention is given to measurement techniques and minimizing potential sources of error.

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Reference: NCERT Lab Manual