Metre Bridge and Potentiometer - UNSOLVED PRACTICE SET

Q7. Draw a labelled diagram of a metre bridge. Explain why it is called a "metre" bridge.

Q8. In a metre bridge experiment, the balance point is found at 40 cm from the left end. The known resistance in the right gap is 12 Ω. Calculate the unknown resistance.

Q9. Why is a potentiometer preferred over a voltmeter for measuring EMF of a cell? Explain the key advantage.

Q10. What is meant by the "potential gradient" of a potentiometer wire? On what factors does it depend?

Q11. A potentiometer wire of length 100 cm has a resistance of 5 Ω. It is connected to a driver cell of 2 V. Calculate the potential gradient.

Q12. Why is it important that the EMF of the driver cell in a potentiometer be greater than the EMF of the cell being measured?

Q13. Explain the principle and working of a metre bridge for measuring unknown resistance. Derive the formula used. Why are thick copper strips used for the gaps and the balance point?

Q14. Explain the principle and working of a potentiometer. Why is it called a "null method" instrument? How does it measure EMF without drawing current from the source?

Q15. In a metre bridge experiment, the unknown resistance X is placed in the left gap and a known resistance R = 10 Ω in the right gap. The balance point is found at 60 cm from the left end.

(a) Calculate the unknown resistance X.

(b) If the resistances are interchanged, where will the new balance point be?

(c) Calculate the resistance of the metre bridge wire if it has uniform resistance per unit length of 0.1 Ω/cm.

(d) Explain why the balance point should ideally be near the middle of the wire for maximum accuracy.

Q16. In your school physics lab, you perform a metre bridge experiment to find the resistance of a wire. The wire is placed in the left gap and a resistance box in the right gap. The following readings are obtained:

Table

R (Ω) Balance point l (cm)

5 75.0

10 60.0

15 50.0

20 42.9

(a) Calculate the unknown resistance X for each reading using the metre bridge formula.

(b) Find the mean value of X and estimate the percentage error.

(c) Plot a graph of (100 − l)/l versus R. What should be the shape of this graph?

(d) From the graph, determine X and compare with the mean value.

(e) Explain why taking multiple readings improves accuracy.

Q17. A potentiometer wire of length 200 cm and resistance 10 Ω is connected to a driver cell of EMF 3 V with internal resistance 1 Ω. A standard cell of EMF 1.08 V is being measured.

(a) Calculate the potential gradient along the wire.

(b) Find the balancing length for the standard cell.

(c) A student cell of unknown EMF E gives a balancing length of 144 cm. Calculate E.

(d) If the driver cell is replaced by one with EMF 5 V, what is the new balancing length for the student cell?

(e) Explain why the potentiometer method gives the true EMF, not just the terminal voltage.

Q18. In a school project, a student builds a potentiometer using a nichrome wire of length 300 cm and diameter 0.5 mm. The wire is connected to a 4 V battery.

(a) Calculate the resistance of the wire. [Given: ρ_nichrome = 1.1 × 10⁻⁶ Ω m]

(b) Calculate the potential gradient.

(c) The student uses this potentiometer to compare the EMFs of two cells. Cell A gives balance at 120 cm and Cell B at 180 cm. Find the ratio E_A/E_B.

(d) If Cell A has internal resistance 0.5 Ω and gives balance at 115 cm when shunted with 10 Ω, calculate the internal resistance using the formula.

(e) Explain why the potentiometer is ideal for comparing EMFs but not for measuring internal resistance directly without a shunt.