EE203 - Measurement Inductance by Maxwell's Bridge and Transient Voltage Method

EE203

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Title: Measurement Inductance by

1.     Using Maxwell’s Bridge

2.     Measuring transient Voltage and time of RL Circuit

Aim: To Measure the value of an unknown inductance L and its resistance (method1) and to find the time (method2)

FIRST METHOD

(Maxwell’s Bridge Method)

Apparatus:

1.     A.F Signal Generator

2.     Two Decade Resistance Boxes

3.     Two Decade Capacitance Boxes

4.     Capacitor of Unknown Value

5.     Head Phones For Circuit Diagram, See Page

For Circuit Diagram, See page 10 on your Electrical Lab Manual

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THEORY:

         The Maxwell's Inductance Bridge is most commonly used bridge for measurement of inductance so f Q value below 10. A typical Maxwell’s bridge consists of an inductance measured in comparison with a capacitance in laboratory operations. The input for the bridge is given through a standard 1 KHz oscillator circuit which produces a 1 KHz sine wave at constant amplitude. The basic circuit diagram is as shown below.

Now let us see the derivation for calculating the unknown value

Let     L4 = Unknown inductance

       R4 = Effective resistance of inductor L1.

       R2, R3, R4 = Known non - inductive resistances

       C2 = Variable standard capacitor.

At balanced condition,

Now separating real and imaginary terms, we have

The expression for Q factor is given by

          The Maxwell's bridge is limited to the measurement of medium Q coils (1<Q<10). This can be shown by considering the second balance condition which states that the sum of the phase angles of one pair of opposite arms must be equal to the sum of the phase angles of the other pair. Since the phase angle of the resistive elements in arm 2 and arm 3 add up to 0, the phase angle of high Q coil will be very nearly positive which requires that the phase angle of the capacitive arm must also be very large indeed which can be very impractical. High Q coil are therefore generally measured on Hay's bridge.

          The main advantage of the bridge is that the two balance equations are independent if we choose R2 and C2 as variable elements and also the frequency does not appear in any of the equations.

          The main disadvantages of the bridge are that it requires a variable standard capacitor which is very expensive so fixed standard capacitors are used normally.

For procedures, see your Electrical Laboratory Manual on pages 10-11

METHOD 2

(By Measuring Transient Voltage)

Apparatus:

1.     A.F Signal Generator

2.     Inductor of unknown value

3.     A Resistor of Unknown Value

4.     An Oscilloscope

For Circuit Diagram, See your Electrical Laboratory Manual on page 11

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THEORY:

It's possible to measure the self inductance of a circuit using a transient technique. This technique uses the exponential current transient to determine the time constant and hence inductance of the coil. While this method can readily provide inductance information about a circuit it does require the use of a digital storage oscilloscope or graphical multimeter. Some of the more advanced multimeters have an inductance measuring facility but if you are serious about investigating and designing coilguns then a good quality DSO should be a high priority on your shopping list. This article describes how to determine the coil's inductance from a trace of its current transient. In order to accurately determine the inductance it is necessary to know the circuit resistance to a reasonable accuracy of say +/- 5%. This is not necessarily easy since the total circuit resistance is usually around 1 or less. Most multimeters only have a resolution of 0.1 and a dedicated ohmmeter is an expensive piece of kit. It is possible to get around this problem by introducing a much larger series resistance into the circuit. For a circuit with an estimated resistance of 1 the additional resistance can be say 100. This resistance then becomes the dominant resistance and we can ignore the resistance of the rest of the circuit. Since the coil is by far the largest inductive component we can solve for this inductance using the following method. Fig 1 shows the main parameters of this inductive circuit. The transient response to a step voltage is governed by the time constant of the circuit and follows an exponential growth according to the function: Eqn 1 The time constant is defined as Eqn 2 where L and R are the circuit inductance and resistance respectively. An important feature of this type of exponential growth is that there are almost exactly 5 time constant periods from the application of the step voltage until the current stablises. What we are interested in is the period of the time constant. This is best determined over the initial part of the exponential curve since it yields a more accurate result. In fact we are only going to consider the very first time constant period. If we solve the exponential current equation above for the first time constant period (t /= 1) then we find that i = 63.2% of maximum. Therefore to find all we need to do is find the time value corresponding to the current at 63.2% of maximum. The trace below is from Test Coil A using a 100 series resistor and a step voltage of 10V. Notice that the voltage markers (horizontal dotted lines) are set to a dV of 6.38V which is 63.8% of the applied 10V. This is the closest value which could be set. The timebase markers (vertical dotted lines) are set to intersect the transient at the points where the voltage markers cut the curve. The resulting dt gives us the time constant for the circuit, in this case it's 19.38us. I typically work with 3 significant figures unless the calculations or experiments demand more. So now we have R=100 and =19.38us therefore the inductance of the circuit is 1.94mH. Since the coil inductance is the dominant inductance then we can say that the coil has an inductance of 1.94mH. It should be remembered that the coil inductance is frequency dependent, so different series resistor values will yield different results. An alternative method of calculating the coil inductance using FEMM is presented here.

PRECAUTIONS:

For Precautions, See General Electrical Lab Precautions

Answers to Questions:

No Questions On This Experiment

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About Uniben Engineering

Stephen Djes is a passionate Graduate of Engineering from the University of Benin, and he is geared towards helping fellow engineering students in the great institution of UNIBEN to do better at academics.