Wheatstone Bridge - UNSOLVED PRACTICE SET

Q7. Draw a labelled diagram of a Wheatstone bridge. Mark the four resistances P, Q, R, S, the galvanometer G, and the battery.

Q8. State the balance condition for a Wheatstone bridge. If P = 10 Ω, Q = 20 Ω, and R = 15 Ω, find the value of S for balance.

Q9. Why is the Wheatstone bridge method more accurate than using an ammeter-voltmeter method for measuring resistance?

Q10. In a Wheatstone bridge, if the galvanometer shows deflection to the left, what does it indicate about the ratio of resistances? How would you achieve balance?

Q11. A Wheatstone bridge has arms P = 5 Ω, Q = 10 Ω, R = 6 Ω, and S = 12 Ω. Is the bridge balanced? If not, which way will the galvanometer current flow?

Q12. Why is the Wheatstone bridge called a "null method"? What are the advantages of a null method over a deflection method?

Q13. Derive the balance condition for a Wheatstone bridge using Kirchhoff's Laws. Show that when P/Q = R/S, the galvanometer current is zero. Draw the circuit diagram and explain each step clearly.

Q14. Explain why the Wheatstone bridge is considered a "null method" of measurement. What are the advantages of this method? Why does the accuracy not depend on the calibration of the galvanometer?

Q15. In a Wheatstone bridge, P = 10 Ω, Q = 15 Ω, R = 6 Ω, and S is unknown. The galvanometer has resistance 20 Ω and the battery has EMF 2 V with negligible internal resistance.

(a) Find the value of S for balance.

(b) Calculate the current through each arm when the bridge is balanced.

(c) If S = 10 Ω (not balanced), calculate the potential difference across the galvanometer and the current through it.

(d) Explain how you would adjust S to achieve balance.

Q16. In a school physics lab, a student sets up a Wheatstone bridge to measure an unknown resistance X. The arrangement uses a resistance box for R, a known resistance Q = 10 Ω, and a ratio arm P = 10 Ω. The student obtains balance when R = 24 Ω.

(a) Calculate the unknown resistance X.

(b) If the ratio arm is changed to P = 100 Ω and balance is obtained at R = 240 Ω, what is X? Verify consistency.

(c) The galvanometer has resistance 50 Ω and sensitivity 10 mm/μA. If the bridge is slightly unbalanced such that R = 24.1 Ω, calculate the galvanometer deflection.

(d) Explain why changing the ratio arm can improve the precision of measurement.

Q17. A modified Wheatstone bridge is used in a strain gauge sensor to measure tiny deformations. The bridge has four resistors: R₁ = R₂ = R₃ = 100 Ω, and R₄ = 100 Ω + ΔR, where ΔR is the small change due to strain.

(a) When ΔR = 0, show that the bridge is balanced.

(b) Derive the expression for the output voltage V_out across the galvanometer when ΔR is small.

(c) If the battery voltage is 5 V and ΔR = 0.5 Ω, calculate V_out.

(d) Explain why this arrangement is very sensitive to small changes in resistance and how it's used in engineering applications.

Q18. A Wheatstone bridge has arms with resistances P = 10 Ω, Q = 20 Ω, R = 15 Ω, and S = 30 Ω. The galvanometer has resistance 40 Ω and the battery has EMF 4 V with internal resistance 1 Ω.

(a) Verify that the bridge is balanced.

(b) Calculate the total current drawn from the battery.

(c) Calculate the current through each arm of the bridge.

(d) If a small resistance δ = 0.1 Ω is added in series with S, calculate the current through the galvanometer.

(e) Show that the bridge is most sensitive when all four arms have equal resistances (or when P = Q and R = S).