Electricity & Electronics 4: The Wheatstone Bridge

Size: px

Start display at page:

Download "Electricity & Electronics 4: The Wheatstone Bridge"

Laurel O’Brien’
6 years ago
Views:

1 Electricity & Electronics 4: The Wheatstone ridge Wheatstone ridge IM In this unit we are going to consider a network of four resistors called a Wheatstone ridge. The principles involved have applications in digital balances, strain gauges, light detectors, smoke detectors, etc. OJECTIES On completing this unit you should be able to: state the relationship among the resistors in a balanced Wheatstone ridge. carry out calculations involving the resistances in a balanced Wheatstone ridge. State that for an initially balanced Wheatstone ridge, as the value of one resistor is changed by a small amount, the out-of-balance pd is proportional to the change in resistance. Use the term bridge circuit correctly in context. Strathaven cademy Electricity and Electronics

2 Wheatstone ridge Wheatstone ridge Circuit ny method of measuring resistance using an ammeter or voltmeter necessarily involves some error unless the resistances of the meters themselves are taken into account. The use of digital voltmeters largely overcomes this as they tend to have very high resistances. Further error may be introduced if the meter is not correctly calibrated. The only situation where neither of these errors matter is if the meter reading is zero. The Wheatstone bridge circuit is one such example of using a meter as a null deflection indicator. ridge Circuit If O = O there is no p.d. between and hence no current flows. The potentials at and at depend on the ratio of the resistors that make up each of the two voltage dividers. The voltmeter forms a bridge between the two voltage dividers to make up a bridge circuit. alanced ridge No potential difference will exist across when O = 3 4 The bridge is balanced when the voltmeter or galvanometer (milliammeter - basically an uncalibrated and very sensitive moving coil meter) reads zero. 1 3 lternative diamond epresentation with galvanometer 2 4 Example The wheatstone bridge circuit shown is balanced. Find the value of x if the other resistors are as shown. 40 Ω 120 Ω How would you know this circuit is balanced? Solution: x 1 3 = 2 40 = x 80 Ω x x =240 Ω You would know the circuit was balanced as the reading on the galvanometer would be zero. Strathaven cademy Electricity and Electronics

3 Wheatstone ridge CTIITY 5 Title: The alanced Wheatstone ridge pparatus: Wheatstone ridge board, 1.5 cell, µ ammeter, 1 kω/10 kω resistance boxes, set of unknown resistances, and C, decade resistance board. 1 K 1 K m e t e r e s i s t a n c e b o a r d U n k n o w n 1 2, & C 1 K e s i s t a n c e o a r d µ 1 K U n k n o w n Schematic diagram showing position of resistances Circuit diagram Instructions Part Connect the decade resistance board and unknown resistance as shown in the diagram above. y finding the value of resistance of the decade resistance board which exactly balances the Wheatstone ridge, find the value of resistance. epeat to find the value of resistances and C. Strathaven cademy Electricity and Electronics

4 Unbalanced ridge Wheatstone ridge If the bridge is initially balanced, and the resistor X is altered by a small amount X then the out of balance p.d. (reading on ) is directly proportional to the change in resistance, provided the change is small. Hence for small X, reading on X eading on X/ Ω X+X 4 NOTE: The change in resistance must be a small fraction of the overall resistance (for example from 1000 Ω to 990 Ω). When set up in this way a Wheatstone bridge can be used to measure any physical quantity that can cause a change in resistance. One of the resistors can be replaced with a sensor such as an LD, a thermistor, a strain gauge and so on. Strathaven cademy Electricity and Electronics

5 Wheatstone ridge CTIITY 7 Title: The Out-of-alance Wheatstone ridge - pplications pparatus: Wheatstone ridge board, 6 battery, µ ammeter, 1 k Ω/10 kω resistance boxes, decade resistance board, LD, thermistor probe, strain gauge (already set up). Instructions Part - Light Meter Connect the circuit up as shown. alance the Wheatstone ridge circuit with the LD on your bench. There is no need to remove the protective resistor as the circuit is quite sensitive. Take care not to cast shadows over the LD when finding balance. Find the out-of-balance current when the LD is in a light place then in a dark place. Explain why the measured current is greater than zero for one condition and less than zero for the other k Ω 1 1 kk Ω e s i s t a n c e o a r d µ L D L D Part -Thermometer Place the probe in an ice/water mixture in a beaker. (0 C) alance the Wheatstone ridge with the probe in the ice/water mixture. Place the probe in a beaker of boiling water. (100 C) Measure and record the out-of-balance current obtained with the probe in the boiling water. Predict the current obtained when the probe is removed and is measuring room temperature. Calculate the value of room temperature from your results. What assumptions are you making about the temperature of the probe, its resistance, and the out-of-balance current? k Ω 1 kkω e s i s t a n c e o a r d p r o b e µ T h e r m i s t o r p r o b e t Strathaven cademy Electricity and Electronics

6 Wheatstone ridge Wheatstone ridges 25. Calculate the p.d. across 2 in each case (a) (b) (c) 2 kω 1 4 kω 500 Ω t +5 8 kω 2 1 kω Ω Calculate the p.d. across (voltmeter reading) in each case. (a) (b) (c) k Ω 5 k Ω 1 0 k Ω 6 k Ω 2 k Ω 8 k Ω 2 k Ω 4 k Ω (a) Calculate the reading on the voltmeter (b) What alteration could be made to balance the bridge circuit? 6 k Ω 9 k Ω 6 k Ω Strathaven cademy Electricity and Electronics

7 Wheatstone ridge 28. Three pupils are asked to construct balanced Wheatstone bridges. Their attempts are shown Ω 10Ω 9Ω 12Ω 7Ω 14Ω 10Ω 5Ω 12Ω 16Ω 10Ω 20Ω Pupil Pupil Pupil C One of the circuits gives a balanced Wheatstone bridge, one gives an out-of-balance Wheatstone bridge and one is not a Wheatstone bridge. (a) (b) (c) Identify each circuit. How would you test that balance has been obtained? In the off balance Wheatstone bridge: (i) calculate the potential difference across the galvanometer. (ii) in which direction will electron current flow through the galvanometer. 29. Calculate the value of the unknown resistor X in each case Ω x 4 k 1 5 k Ω Ω Ω 9 Ω 1 2 k x Ω 30. The circuit shown opposite is balanced. 1 0 k Ω 2 5 k Ω 3.6 k Ω x (a) What is the value of resistance? 1 0 Ω 2 0 Ω (b) Will the bridge be unbalanced if (i) a 5 Ω resistor is inserted next to the 10 Ω resistor (ii) a 3 supply is used. (c) What is the function of resistor and what is the disadvantage of using it as shown? 5 Ω X Strathaven cademy Electricity and Electronics

8 31. The following Wheatstone bridge circuit is used to monitor the mechanical strain on a girder in an oil rig Wheatstone ridge S train gauges (a) (b) Explain how the circuit can be used to monitor the strain. Sketch the graph of current through the galvanometer against the strain n automotive electrician needed to accurately measure the resistance of a resistor. She set up a circuit using an analogue milliammeter and a digital voltmeter. The two meter readings were: m OO1.3 (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) (l) (m) What are the readings? What is the nominal resistance calculated from these readings? Which reading is likely to cause the greatest uncertainty? What is the smallest division on the milliammeter? What is the absolute uncertainty on the milliammeter? What is the absolute uncertainty on the voltmeter? What is the percentage uncertainty on the milliammeter? What is the percentage uncertainty on the voltmeter? Which is the greatest percentage uncertainty? What is the percentage uncertainty in the resistance? What is the absolute uncertainty in the resistance? Express the final result as (resistance ± uncertainty)ω ound both the result and the uncertainty to the relevant number of significant figures or decimal places. Strathaven cademy Electricity and Electronics

Sensing Devices. Question Paper. Save My Exams! The Home of Revision. International A Level. Exam Board. Current of Electricity.

Sensing Devices. Question Paper. Save My Exams! The Home of Revision. International A Level. Exam Board. Current of Electricity. For more awesome GSE and level resources, visit us at www.savemyexams.co.uk/ Sensing evices Question Paper Level Subject Exam oard Topic Sub Topic Paper Type ooklet International Level Physics IE urrent