Resistance of a wire using a metre bridge (Class 12 practical)

Aim

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

Apparatus and material required

• •Metre bridge
• •The given wire (or standard resistor) of unknown resistance
• •Resistance box
• •Galvanometer
• •Jockey
• •One-way key
• •Rheostat
• •Cell or battery eliminator
• •Thick connecting wires and sandpaper

Principle

Metre bridge: resistance of a wire: formulas and key facts

Wheatstone bridge balance

$\frac{P}{Q}=\frac{R}{S}$

Unknown in the left gap

$S_1=R\frac{l}{100-l}$

l is the balancing length from end A (the end on the side of S), in cm.

Unknown in the right gap (interchanged)

$S_2=R\frac{100-l^{\prime }}{l^{\prime }}$

l' is the new balancing length, still measured from end A.

Mean resistance

$S=\frac{S_1+S_2}{2}$

Key facts

• •Metre bridge wire: usually constantan or manganin
• •Wire must have uniform cross-section
• •Null point is best near the middle (30 cm to 70 cm)
• •Bridge is most sensitive when all four arms are of the same order
• •Balance does not depend on the cell's emf
• •Touch the jockey gently; do not slide it while pressed

Procedure

1. 1Clean the ends of the connecting wires with sandpaper. Press every plug of the resistance box in tightly.
2. 2Connect the unknown wire S in the left gap and the resistance box R in the right gap. Connect the cell, key and rheostat across the ends A and C of the bridge wire, and the galvanometer between the middle terminal B and the jockey.
3. 3Take out a plug to introduce a suitable resistance R. Touch the jockey at end A and then at end C. If the deflections are in opposite directions, the null point lies on the wire; if they are in the same direction, check the connections.
4. 4Adjust R so that the null point is between 30 cm and 70 cm. Touch the jockey gently at different points to find the point D where the galvanometer shows no deflection. Note the balancing length l = AD.
5. 5Repeat for four more values of R (five readings in all).
6. 6Interchange S and R, keeping the same length of wire in the gap. Repeat steps 3 to 5 for the same values of R and note the balancing lengths l'.
7. 7Calculate S for each reading and take the mean.

Observation table

Draw the table like this in your record. The numbers are sample readings to show how it is filled in; use your own.

Calculation

1. 1.Row 3, S in the left gap: $S_1=\frac{4\times 43.0}{57.0}=3.018\approx 3.02\Omega$
2. 2.Row 3, interchanged: $S_2=\frac{4\times 42.8}{57.2}=2.993\approx 2.99\Omega$ (here 100 − l' = 42.8 and l' = 57.2); row mean = 3.01 Ω
3. 3.Mean of the five row means: $S=\frac{3.01+3.00+3.01+3.00+3.00}{5}=3.004\approx 3.00\Omega$ (the mean of all ten values, 3.003 Ω, gives the same 3.00 Ω to 3 significant figures)

Result

The resistance of the given wire is S = ____ Ω (sample: 3.00 Ω).

Precautions

• →All connections and plugs must be tight and clean.
• →Insert the key only while taking a reading, so the wire does not heat up.
• →Touch the jockey gently on the wire; never slide it while pressed, or the wire loses its uniform cross-section.
• →Choose R so that the null point lies between 30 cm and 70 cm.
• →When interchanging S and R, keep the same length of the unknown wire in the gap.

Sources of error

• •The bridge wire may not have a uniform cross-section.
• •The copper strips, terminals and screws have small end resistances (reduced by interchanging S and R).
• •The bridge wire may not be taut or exactly along the scale, so lengths are misread.
• •The resistance box values may not be exactly what is marked on it.
• •A galvanometer pointer not set at zero makes the null point uncertain.

Viva questions with answers

Say your answer out loud first, then open the card. Examiners want one or two clear sentences, not a paragraph.

1. 1.On what principle does a metre bridge work?Show answer

   The Wheatstone bridge principle: at balance, with no current through the galvanometer, P/Q = R/S.

2. 2.Why is it called a metre bridge?Show answer

   Because the bridge wire is one metre long.

3. 3.Of what material is the bridge wire made, and why?Show answer

   Constantan or manganin. They have a high resistivity and a low temperature coefficient of resistance, so the wire's resistance hardly changes as it warms.

4. 4.Why should the null point be near the middle of the wire?Show answer

   The bridge is most sensitive there, and the end resistances and the error in reading l have the least effect on the result.

5. 5.What are end resistances, and how do you reduce their effect?Show answer

   The small resistances of the copper strips, terminals and the joins at the ends of the wire. Their effect is reduced by interchanging S and R and taking the mean.

6. 6.Why are thick copper strips used in a metre bridge?Show answer

   They have negligible resistance, so almost all the resistance of the arms comes from the bridge wire and the resistors in the gaps.

7. 7.Does the null point change if the cell's emf is changed?Show answer

   No. The balance condition P/Q = R/S does not involve the emf; a larger emf only makes the null point easier to detect.

8. 8.Can the galvanometer and the cell be interchanged?Show answer

   Yes. The balance condition stays the same, so the null point does not change.

9. 9.Why should the jockey not be slid along the wire while pressed?Show answer

   It scrapes the wire, so its cross-section is no longer uniform, and resistance is then not proportional to length.

10. 10.Why is a metre bridge not suitable for very low or very high resistances?Show answer

    The null point would be very close to one end, where the end resistances and reading errors are large compared with the balancing length.

11. 11.What is the use of the rheostat in the circuit?Show answer

    It limits the current through the bridge wire, so the wire does not heat up.

12. 12.What is a null point?Show answer

    The point on the bridge wire where touching the jockey gives no deflection in the galvanometer.

Viva practice: these questions one at a time, with the answer hidden until you ask, and a tally of what to revise.

Common mistakes in the practical exam

The slips examiners see most often, and what to write instead.

• ✗Mistake: Using S = R(100 − l)/l with S in the left gap.

  The ratio is upside down, so S comes out wrong unless l happens to be 50 cm.

  ✓Do this: Write the ratio from your own diagram: the length on the side of S goes on top of the side of R.

• ✗Mistake: Measuring l from the wrong end after interchanging.

  ✓Do this: Always read l from end A, and use $S_2=R(100-l^{\prime })/l^{\prime }$ when S is in the right gap.

• ✗Mistake: Choosing R so that the null point is at 5 cm or 95 cm.

  ✓Do this: Change R until the null point is between 30 cm and 70 cm before taking a reading.

• ✗Mistake: Leaving the key in throughout.

  ✓Do this: Close the key only while you look for the null point, so the wire stays cool.

• ✗Mistake: Drawing the circuit diagram without the rheostat, key or the direction of the cell.

  ✓Do this: Draw every component with standard symbols and label the gaps, A, C, B, D and G.

Metre bridge: resistance of a wire: frequently asked questions