Expt02 - Verification Of Kirchhoff's Laws 2h4d1n

Basics of Electrical and Electronic Circuits Experiment 2

Monsoon 2016

Verification of Kirchhoff’s Laws It is important to that Kirchhoff’s Laws are applicable to any electrical circuit, irrespective of the characteristics of the circuit elements including the sources. Just to emphasise this fact, the circuit we will use in this experiment will consist of three linear resistors, a linear capacitor and a diode (nonlinear resistor), with an independent voltage source applied either from the Function Generator or from the WAVEGEN built in the Agilent DSO, referred henceforth as FG, as shown in Fig. 2.1. a, b, c and d denote four nodes of the circuit, and the Ground symbol ( ) indicates the common reference node for voltages. The voltages at the four nodes with respect to Ground will be denoted by va, vb, vc and vd, and the voltages between two adjacent nodes by vab, vbc and vcd respectively. The currents i1, i2 and i3 indicated in the circuit diagram are then given by Ohm’s Law as follows: i1 = vab / R1, i2 = vc / R2 and i3 = vd / R3. All the voltages and currents in the different elements constituting the circuit can thus be obtained from the node voltages between these nodes, measured with a Digital Storage Oscilloscope (DSO). Verification of KVL will be done for the loop Gnd-a-b-c-Gnd, and will involve the measurement of the instantaneous values of voltages at different instants of time and ing that va – vac –vc = 0 at each selected instant. Verification of KCL will be done for node c, and will involve the determination of the instantaneous values of the currents i1, i2 and i3 from the measured voltages at different instants of time and ing that i1 – i2 – i3 = 0 at each selected instant. Experimental Steps a

b R1

FG

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5. 6. 7.

i1

c

C d

D

i3 R2

i2

R3

1. Assemble the circuit given in Fig. 2.1 on the breadboard using the following given components: three ¼W 1.2k resistors as R1, R2 and R3, one 0.1F polyester capacitor as C, one 1N4007 rectifier diode as D.

Fig. 2.1 Connect the Ground leads (black wire) of the DSO and the FG to the Ground line at the bottom strip of the breadboard. Connect Channel 1 Input of the DSO and the FG output to node a of the circuit. Switch on the DSO and set its Trigger Source as Channel 1 with positive slope. Set the FG for a 1kHz TRIANGULAR wave output having PEAK-TO-PEAK voltage 5V with an OFFSET +2.5V. Adjust the DSO controls so that the display shows one full cycle of the FG output vs on full scale, with the time origin (t = 0, centre of the screen) set at the midway point of the rising part of the waveform Measurement of the relevant voltages and consequent verification of Kirchhoff’s laws will be carried out at 4 instants of time t1 = – 0.4ms, t2 = – 0.2ms, t3 = 0.1ms and t4 = 0.3ms. These points have been selected so that they lie in four different regions of the waveform: (i) the first quarter (negative slope), (ii) the second quarter (positive slope), (iii) the third quarter (positive slope) and (iv) the fourth quarter (negative slope) respectively. Make a table with 5 columns for the voltages va, vac, vcd, vc and vd and 4 rows for the four time instants t1, t2, t3 and t4. The voltage readings will have to be entered in this table. Adjust the horizontal position so that the point t = t1 lies on a vertical line of the graticule. Connect Channel 2 Input of the DSO to node b, node c and node d one by one, and measure the instantaneous values of va, vab, vac, vc and vd at t = t1 with the help of the horizontal cursors. Note that while va, vc and vd can be directly measured from their displayed waveforms, vab and vac have to be measured by using the Mathematical function CH1 – CH2 available on the DSO, with the Channel 2 input connected to vb and vc respectively. Repeat step 4 for the other three time instants t2, t3 and t4 one by one. KVL by ing that va – vac – vc = 0 at all the 4 instants of time t1, t2, t3 and t4. Note that as R1 = R2 = R3, the relationship i1 – i2 – i3 = 0 required by KCL is equivalent to the relationship vab – vc – vd = 0. this at all the 4 instants of time taken for the measurements.