FCULTY OF ENGINEEING LB SHEET EEL96 Instrumentation & Measurement Techniques TIMESTE 08-09 IM: Wheatstone and Maxwell Wien Bridges *Note: Please calculate the computed values for Tables. and. before the lab session. These two tables will be checked during your lab session. On-the-spot evaluation will be carried out during or at the end of the experiment. Students must read through this lab sheet before doing the experiment. Your performance, teamwork effort, and learning attitude will count towards the marks.
Wheatstone and Maxwell Wien Bridges Precautionary steps: ead the lab sheet thoroughly and carefully before coming to your lab session. Take precautions for safety. lso handle the equipments carefully to prevent any damages. Try to get as much of the analysis done during the lab session. Objectives: To be able to construct the basic Wheatstone bridge measure voltages in an unbalanced bridge for different configurations and verify the unknown resistors. To be able to construct the Maxwell Wien bridge to measure the values of unknown resistance and inductance. pparatus: DC power supply Breadboard Digital Multimeter Function Generator resistors of. k ± 5%. resistors of. k resistor each of 5, k, 0 k and.7 k. potentiometers of 5 k,0 k and 00 k inductor of.5mh. capacitor of 0nF Part I. WHETSTONE BIDGE. Theory 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. 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 =, for the circuit of Figure. is satisfied, the bridge is balanced and a null or zero reading is obtained on the detector. Consider the Wheastone's bridge shown in Fig... It has four arms each having a resistance. The voltage at the nodes and B may be computed using the simple potential division rule as below: V. (.) V V S (.) B V S
The voltage across the nodes and B measured in the voltmeter would equal the difference between the voltages at nodes and B: VB V -VB = VS - VS (.) When the Wheatstone's bridge is balanced, the voltage VB would equal zero. Thus in that condition, equating VB to zero in equation (.), one gets: V B = VS - VS = 0 (.) On re-arranging, one gets: =. (.5) Thus one may derive: = (.6) V S V B B Figure.: Wheatstone Bridge Circuit. Error Percent of error for every reading taken against the computed values using the formula given below: % error measured - calculated calculated 00%
Part : Procedure:. Construct the Wheatstone's bridge according to the circuit diagram given in Figure., where = = =. k.. Switch on the DC power supply and adjust the variable voltage source to show VS = V.. Measure the voltage across the point & B and determine the % error between the measured and the computed values according to the resistor values given in Table.. esistance, () k.k.k Table. VB (volts) Computed Measured % error Part B: Procedure:. Construct the Wheatstone's bridge according to the circuit diagram given in Figure., where =. k, =. k, (variable resistor) = 5 k and Vs = V.. For every value of given in Table., adjust the variable resistance until the bridge is balanced. (Hint: value of VB reduces to zero or smallest possible value). Measure the value of and tabulate the readings in Table... Compute the expected value, c for every value of given in Table.. 5. Determine the percentage error (%error) for every reading taken against the computed values. esistance,.k.k.7k Computed value of Table. c Measured value of when VB 0 volts % error (Hint: Verify the given resistor value)
Part II. MXWELL-WIEN BIDGE. Theory: The C 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 C 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. i i Vac D B Figure. General C Bridge The general form of an ac bridge is given in Fig... The four bridge arms,,, and 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 to B be zero. This happens when the voltage at node equals the voltage at node B, in both magnitude and phase. In complex notation we can write V V V V ; and i i i i Dividing the equation, (.) (.) If the impedances are written in polar form,, where represents the magnitude and the phase angle of the complex impedance. Equation(.) can be rewritten as ( (.) )( ) ( )( ) (.) 5
To multiply these complex numbers we multiply the magnitudes and add the phase angles. Thus, equation (.) can be rewritten as ) ( ) (.5) ( Equation (.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 (.6) The second condition requires that the phase angles of the impedances satisfy the relationship (.7) This expression states that the sums of the phase angles of the opposite arms must be equal. Maxwell Wien Bridge The Maxwell Wien bridge shown in Fig.. measures an unknown inductance in terms of a known capacitance. Observing the bridge, we can see that and jw C ; ; x jwl x Substituting these expressions into Equation (.6) and separating the real and imaginary terms yields x (.8) L x C (.9) Both Equations (.8) and (.9) must be satisfied for the bridge to be balanced. C Vin G B X LX Figure. Maxwell Wien Bridge. 6
. 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. However, a lossy 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. Q X s X (.0) s L X where LS and S, refer to the components of an L series equivalent circuit. Q-factors for typical inductors range from a low of less than 5 to as high as 000 (depending on frequency).. Procedure:. Construct the ac bridge according to the circuit diagram shown in Fig.. with the following components: C = 0 nf (variable resistor) = 00 k (variable resistor) = 0 k = 5 Inductor, L =.5 mh (Hint: Verify the given C and values). By using the function generator, generate a 0 khz sinusoidal signal with Vpp = V supply across the bridge circuit. (Hint: use the oscilloscope to determine the supply Vpp). Balance the bridge by varying the resistors (from 5k to 95k) and (from k to 9k).. emove and from the circuit and measure and record their values into Table.. 5. Compute the parameters given in Table. accordingly. 6. Measure the dc resistance of the inductor, x. 7. Compute the percentage of error between the measured and computed values of x. Table. No. Parameter Computed Measured % Error LX X 5 Q 6 X 7 X 7
. EXECISE: a) Explain the term 'sensitivity of the bridge'. b) For each measurement in part I (B), determine whether V > VB or V < VB. Explain to support your answers. c) In part II, (i) By using the computed Lx and x, compute the total impedance of the inductor using the expression X X L X X L and tan. X (ii) Given that the resistor of and capacitor C available in the laboratory is 00 and 0.5 nf respectively. Evaluate your setup in part II to determine the component values of the variable resistor and to balance the computed Lx and x values in the Maxwell Wien bridge.. GUIDELINE FO LB EPOT ND SUBMISSION: a) The report must be handwritten and should contain the following: Objective of the experiment. Basic theory and schematic diagrams. Tabulation of the observed and computed data. nswers to the exercise questions. Your own results and conclusions. b) ll reports must be neatly handwritten. Neatness and carefulness are counted. Typewritten report will not be accepted under any circumstances. c) Write your own report and use your own findings and results, similar reports won t be given marks for both the original and the copied ones. d) Duration of lab report submission: not more than ONE WEEK after the date of your experiment. e) Late submission of your lab report will result in deduction of marks (0.5 marks per day of late submission). 8