FACULTY OF ENGINEERING

LAB SHEET

EPM1016Instrumentation & Measurement Techniques

TRIMESTER 2 2012-2013

IM1: Wheatstone and Maxwell Bridges

Wheatstone and Maxwell Bridges

Precautionary steps:

  • Read thelab sheet thoroughly and carefully before coming to your lab session.
  • Take precautions for safety. Also handle the equipments carefully to prevent any damages.
  • Try to get as much of the analysis done during the lab session.

Objectives:

  • Construct the basic Wheatstone bridge measure voltages in an unbalanced bridge for different configurations and verify the unknown resistors.
  • Construct the Maxwell bridge tomeasure the values of unknown resistance and inductance ofan inductors.

Apparatus:

  • DC power supply.
  • Breadboard
  • Digital Multimeter
  • Function Generator.
  • 4 resistors of 2.2 k ± 5%.
  • 2 resistors of 3.3 k
  • 1 resistor each of 51, 1 k, 10 k and 4.7 k.
  • 3 potentiometers of, 5 k,10 k and 100 k
  • 1 inductor of 2.5mH.
  • 1 capacitor of 10nF

Part I. WHEATSTONE BRIDGE

1.1Theory

The basic Wheatstone bridge has been used extensively since the earliest days of electricity. It is still widely used in a large number of null-type instruments. A null reading is obtained on a Wheatstone bridge by a comparison of the voltage drops in the passive resistance arms of the bridge. When the equation R1R4 = R2R3, for the circuit of Figure 1.1 is satisfied, the bridge is balanced and a “null” or zero reading is obtained on the detector.

Consider the Wheastone's bridge shown in Figure 1.1. It has four arms each having a resistance. The voltage at the nodes A and B may be computed using the simple potential division rule as below:

(1.1)

(1.2)

The voltage across the nodes A and B measured in the voltmeter would equal the difference between the voltages at nodes A and B:

= -(1.3)

When the Wheatstone's bridge is balanced, the voltage VAB would equal zero. Thus in that condition, equating VAB to zero in equation (1.3), one gets:

= -= 0(1.4)

On re-arranging, one gets:= . (1.5)

Thus one may derive:

R1R4 = R2R3(1.6)

1.2 Error

Percent of error for every reading taken against the computed values using the formula given below:
Part A:

Procedure:

  1. Construct the Wheatstone's bridge according to the circuit diagram given in Figure 1.1, where R1 = R2 = R3 = 2.2k.
  2. Switch on the DC power supply and adjust the variable voltage source to show VS = 12V.
  3. Measure thevoltage across the point A andB,then, determine the %error between the measured and the computed values according to the resistor values given in Table 1.1.
Table 1.1
Resistance, R4() / VAB (volts)
Computed / Measured / % error
1k
2.2k
3.3k

Part B:

Procedure:

  1. Construct the Wheatstone's bridge according to the circuit diagram given in Figure 1.1, where R1 = 3.3k, R2 = 2.2k, R4 (variable resistor) = 5 k and Vs = 12V.
  2. For every value of R3given in Table 1.2, adjust the variable resistance R4 until the bridge is balanced. (Hint: value of VAB reduces to zero or smallest possible value)
  3. Measure the value of R4 and tabulate the readings in Table 1.2.
  4. Compute the expected value, for every value of R3given in Table 1.2.
  5. Determine the percentage error (%error) for every reading taken against the computed values.
Table 1.2
Resistance, R3 / Computed value of / Measured value of R4 when VAB 0 volts /
2.2k
3.3k
4.7k

(Hint: Verify the given resistor value)

Part II.MAXWELLBRIDGE

2.1Theory:

The AC Bridge, a natural outgrowth of the DC bridge, consists in its basic form of four bridge arms, a source of excitation, and a null-detector. The source of excitation is an AC signal at the desired frequency. The detector may be a set of an ac voltmeter, an oscilloscope, or another device capable of responding to alternating currents.

The general form of an ac bridge is given in Fig. 2.1. The four bridge arms Z1, Z2, Z3, and Z4 are shown as unspecified impedances. The bridge is said to be balanced when the detector response is zero. One or more of the bridge arms are varied to balance the bridge so that a null response is obtained. The condition for bridge balance requires that the potential difference from A to B be zero. This happens when the voltage at node A equals the voltage at node B, in both magnitude and phase. In complex notation we can write

; and (2.1)

Dividing the equation,

(2.2)

(2.3)

If the impedances are written in polar form, Z, where Z represents the magnitude and  the phase angle of the complex impedance. Equation(2.3) can be rewritten as

(2.4)

To multiply these complex numbers we multiply the magnitudes and add the phase angles. Thus, equation (2.4) can be rewritten as

(2.5)

Equation (2.5) shows that two conditions must be met simultaneously when balancing an ac bridge. The first condition is that the magnitude of the impedances satisfy the relationship

(2.6)

The second condition requires that the phase angles of the impedances satisfy the relationship

(2.7)

This expression states that the sums of the phase angles of the opposite arms must be equal

2.2 MaxwellBridge

The Maxwell bridge shown in Fig. 2.2 measures an unknown inductance in terms of a known capacitance. Observing the bridge, we can see that

Substituting these expressions into Equation (2.6) and separating the real and imaginary terms yields

(2.8)

(2.9)

Both Equations (2.8) and (2.9) must be satisfied for the bridge to be balanced.

2.3 Q-factor of an Inductor

The quality of an inductor is defined in terms of its power dissipation. For an ideal inductor, the winding resistance should have zero resistance, and hence zero power dissipated in the winding. For alossy inductor which has a relatively high winding resistance, dissipates some power. The quality factor or Q-factor of the inductor is the ratio of the inductive reactance and resistance at the operating frequency f.

(2.10)

where LS and RS, refer to the components of an RL series equivalent circuit. Q-factors for typical inductors range from a low of less than 5 to as high as 1000 (depending on frequency).

2.4 Procedure:

  1. Construct the ac bridge according to the circuit diagram shown in Fig. 2.2 with the following components:
  • C1 = 10 nF
  • R1 (variable resistor) = 100 k
  • R2 (variable resistor) = 10 k
  • R3 = 51 
  • Inductor, L = 2.5 mH

(Hint: Verify the given C1 and R3 values)

  1. By using the function generator, generate a 10kHz sinusoidal signal with Vpp = 12V supply across the bridge circuit. (Hint: use the oscilloscope to determine the supply Vpp)
  2. Balance the bridge by varying the resistors R1 (from 5k to 95k) and R2 (from 1k to 9k).
  3. Remove R1 and R2 from the circuit and measure and record their values into table 2.1.
  4. Compute the parameters given in Table 2.1 accordingly.
  5. Measure the dc resistance of the inductor, Rx.
  6. Compute the percentage of error between the measured and computed values of Rx.

Table 2.1

No. / Parameter / Computed / Measured / % Error
1 / R1
2 / R2
3 / LX
4 / RX
5 / Q
6 / ZX
7 / RX

3. EXERCISE:

a)Explain the term 'sensitivity of the bridge'.

b)For each measurement in part I (B), determine whether VA > VB or VA VB. Explain to support your answers.

c)In part II experiment,

(i)By using the computed Lx and Rx, compute the total impedance of the inductor using the expression and .

(ii)If the resistor of R3and capacitor C1available in the laboratory is 100  and 0.5 nF respectively. Evaluate your setup in part II to determine the component values of the variable resistor R1 and R2to balance the computed Lx and Rx values in the Maxwell bridge.

4. GUIDELINE FOR LAB REPORT AND SUBMISSION:

a)The report should contain the following:

  • Objective of the experiment.
  • Basic theory and schematic diagrams.
  • Tabulation of the observed and computed data.
  • Answers to the exercise questions.
  • Conclusions.

b)You are given ONE WEEK to prepare and submit your lab report to the lab staff.

c)All reports can be handwritten or typed. Neatness and carefulness will be taken into account in the marking of your report.

d)You MUST use the FOE lab report cover template. The template can be downloaded at

e)Prepare your own lab report and use your own findings and results.

f)Please be instructed that plagiarism is an academic offence and if similar reports are found, you should be required to give an explanation for the similarities and no marks will be given for both the original and the copied ones.

g)Late submission of your lab report will not be usually entertained unless if there is any emergency cases and strong proof for late submission. Otherwise, automatically awarded 0 (zero) mark for the late submission.

h)This lab report carries 5% of the total course marks.

MARKING SCHEME

Total: 50% scale to 5%

  1. Report content (Objective, theory and conclusions) – 10%
  2. Experiment Results (observed and computed data) – 30%
  3. Exercise – 10%

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