# Wheatstone bridge Numerical questions and Solutions – Electrical Measurements

# 1. The measurement of an unknown resistance R is to be carried out using the Wheatstone bridge. Two students perform an experiment in two ways. The first student takes R_{2} = 10Ω and R_{1} = 5Ω. The other student takes R_{2} = 1000Ω and R_{1}= 500Ω. In the standard arm, both take R = 5Ω. Both find R = (R_{2}/R_{1})R_{3} = 10Ω within errors.

- The errors of measurement of the two students are the same.
- Errors of measurement do depend on the accuracy with which R
_{2}and R_{1}can be measured. - If the student uses large values of R
_{2}and R_{1}the currents through the arms will be feeble. This will make the determination of null point accurately more difficult. - Wheatstone bridge is a very accurate instrument and has no error in measurement.

# 2. Four arms of a Wheatstone bridge are as follows: AB = 100 Ω, BC = 10 Ω, CD = 4 Ω, DA = 50 Ω. A galvanometer with an internal resistance of 20 Ω is connected between BD, while a battery of 10-V dc is connected between AC. Find the current through the galvanometer.

- 6.24 mA
- 5.18 A
- 5.18 mA
- 51.8 mA

# 3. Four arms of a Wheatstone bridge are as follows: AB = 100 Ω, BC = 10 Ω, CD = 4 Ω, DA = 50 Ω. A galvanometer with an internal resistance of 20 Ω is connected between BD, while a battery of 10-V dc is connected between AC. Find the value of the

resistance to be put on the arm DA so that the bridge is balanced

- 40 Ω
- 50 Ω
- 20 Ω
- 10 Ω

# 4. In a Wheatstone’s bridge P = 50 Ω, Q = 100 Ω and R = 20 Ω. If the galvanometer shows zero deflection, determine the value of S.

- 20 Ω
- 40 Ω
- 50 Ω
- 25 Ω

# 5. The four arms of a Wheatstone bridge are as follows: AB = 100 Ω, BC = 1000 Ω, CD = 4000 Ω, DA = 400 Ω. A galvanometer with an internal resistance of 100 Ω and a sensitivity of 10 mm/μA is connected between AC, while a battery of 4 V dc is connected between BD. Calculate the deflection if the resistance of arm DA is changed from 400 Ω to 401 Ω.

- 20.4 mm
- 204 mm
- 2.04 mm
- 0.204 mm

# 6. What is the value of *x* when Wheatstone’s network is balanced?

# P = 500 Ω, Q = 800 Ω, R = *x* + 400, S = 1000 Ω

- 200Ω
- 250Ω
- 150Ω
- 225Ω

# 7. A Wheatstone bridge has P = 3.5 kΩ, Q = 7 kΩ, and galvanometer null is obtained when S = 5.51 kΩ. Determine the resistance measurement range for the bridge if S is adjustable from 1 kΩ to 8 kΩ.

- 500Ω to 400Ω
- 4Ω to 500Ω
- 500Ω t0 4Ω
- 50Ω to 40Ω

# 8. In Wheatstone’s bridge arrangement PQRS, the ratio arms P and Q are nearly equal. The bridge is balanced when R = 500Ω. On interchanging P and Q, the value of R for balancing is 510Ω. Find the value of S.

- 510.58Ω
- 504.97Ω
- 525.24Ω
- 425.22Ω

# 9. Four resistances 4Ω, 8Ω, XΩ and 6Ω are connected in a series so as to form Wheatstone’s network. If the network is balanced, find the value of ‘X

- 5Ω
- 10Ω
- 1Ω
- 3Ω

10. Resistances in the branches of Wheatstone’s bridge are 30Ω, 60Ω, 15Ω and a series combination of X and 5Ω resistances. If the bridge is balanced then value of unknown resistance X is

- 50Ω
- 40Ω
- 25Ω
- 15Ω