ESP1104 Introduction to Electronic Systems Khursheed
Tutorial 2
1) You connect a voltmeter to a 1 μF capacitor and measure zero volts, and conclude that the capacitor is discharged. You leave the voltmeter connected to the
capacitor. You now connect the terminals of a 9V battery across the capacitor and then disconnect it. You notice that the voltage indicated on the voltmeter jumps quickly up to 9V on connecting the battery, but takes a relatively long time to drop after the disconnection, taking 32 seconds to drop to 1V.
a) Derive an expression for the time constant of charge up, τ1 and the time constant of discharge τ2, in terms of the battery internal resistance, Rb, and voltmeter internal resistance Rm .
b) Explain why the charge up and discharge times are very different. c) Estimate the internal resistance of the voltmeter.
2) You want to investigate the output time response of a signal generator, so you connect it to an oscilloscope via a coaxial cable. The signal generator can be modeled as a voltage source with an internal resistance RS which has a capacitance CS across its output terminals, and from the signal generator
handbook, you find RS is 50 Ω. You also see from the handbook that the rise time (time taken between 10% to 90% of the signal final height) is 12 ns.
a) Calculate the expected output capacitance of the signal generator according to the handbook data.
b) You use a 1 kHz square wave and measure the time taken for the signal to reach 50% of its maximum height to be 12 ns on the oscilloscope display. How close is the capacitance of the measured time response to that predicted from the handbook?
c) You consult a handbook and find that the oscilloscope has an input capacitance of 15 pF across its terminals, and an input resistance of 1 M Ω in parallel with it. Is this enough to explain the discrepancy between the expected capacitance from the handbook and that obtained by
measurement? If not, what else might be contributing to the error?
3) Determine an expression for VR(t) for the circuit shown below. Assume that prior to the switch being opened at t = 0, the circuit had reached a steady-state condition (with the switch in the closed position). Plot VR(t) to scale for the time interval -0.2 < t < 1 ms (use at the most, only ten points).
10 Ω
0.2 H + 1 kΩ
- VR(t)
10 V
