THE HONG KONG POLYTECHNIC UNIVERSITY
Department of Electronic and Information Engineering
ENG237-E03r1
ENG237-E03: Transients in RC and RL Circuits
Introduction
The objective of this experiment is to study the DC transient behaviors of RC and RL
circuits.
(a) Capacitor
A capacitor is a device that stores energy in the electric field created by a pair of
conductors on which equal but opposite electric charges have been placed. The circuit
symbol of a capacitor is shown below.
For an ideal capacitor, the capacitor current iC is proportional to the time rate of change of
the voltage across the capacitor:
Where C is the proportionality constant and is known as capacitance.
(b) Inductor
An inductor is designed to store energy in its magnetic field. Any conductor of electric
current has inductive properties and may be regarded as an inductor. But in order to
enhance the inductive effect, a practical inductor is usually formed into a cylindrical coil
with many turns of conducting wire. The circuit symbol for an inductor is shown below.
For an ideal inductor, the inductor voltage VL is proportional to the time rate of change of
the current through the inductor:
Where L is the proportionality constant and is known as inductance.
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THE HONG KONG POLYTECHNIC UNIVERSITY
Department of Electronic and Information Engineering
ENG237-E03r1
Apparatus
1. Experimental board
2. Square wave generator
3. Oscilloscope
4. Digital voltmeter
5. DC power supply
6. Stop watch
Procedure
1. Charging curve from measured data
(a) Use the digital voltmeter V to measure the supply voltage VS. Do not change the range
of the voltmeter after the supply voltage of 5 V has been obtained. Record the supply
voltage VS.
(b) Use the digital voltmeter V in (a) and connect the circuit as shown in Figure 1, with R
= 10 MΩ, C = 4 µF, and the Switch SW to position 2.
(c) With the stop watch at “ready”, switch SW from position 2 to position 1 and at the
same instant start the stop watch. Record the capacitor voltage at suitable intervals (at
least 8) until the capacitor is fully charged, as shown by a steady maximum voltage.
(d) Plot the charging curve (volts on the vertical axis) on a graph paper.
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THE HONG KONG POLYTECHNIC UNIVERSITY
Department of Electronic and Information Engineering
ENG237-E03r1
2. Draw the charging curve by the graphical method (no measurement is needed). The
circuit in Figure 1 can be represented by its equivalent circuit shown in Figure 2,
where, RC is the equivalent resistance of R in procedure 1 and the internal resistance, r,
of the voltmeter. The internal resistance of the DVM = 10 MΩ, so
Refer to Electrical Technology by E. Hughes, p.166 for detail graphical method. Draw the
curve on the same graph paper as in step 1 (d).
3. Charging curve from measured data
(a) Connect the circuit as shown in Figure 1, with R = 5 MΩ (by connecting two 10 MΩ
resistors in parallel) and C = 4 µF. Switch SW to position 1. Wait for three minutes
until the capacitor is fully charged.
(b) Calculate the equivalent charging voltage.
(c) Change the switch from position 1 to position 2 and at the same instant start the stop
watch.
(d) Record the capacitor voltage at suitable intervals to plot the decay curve of the
capacitor voltage.
4. Graphical construction of discharge curve
On the same graph paper as in step 3(d), plot the discharge voltage curve using the
graphical method.
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THE HONG KONG POLYTECHNIC UNIVERSITY
Department of Electronic and Information Engineering
ENG237-E03r1
5. Display of the charging and discharging curve
(a) Connect a circuit as shown on Figure 3.
(b) Use Figure 3, a 300-Hz square wave input (2 volt peak to peak) and record the
waveform observed on the oscilloscope.
6. Display of the charging and discharging curve
(a) Circuit diagram
(b) When a step voltage V is applied across an RL series circuit the inductor current may
be obtained by the relation:
(c) Use the circuit above and record the waveform of the inductor voltage, VL, as shown
on the CRO.
(d) Obtain the curve of the resistor voltage (iLR) by subtracting the VL curve from the DC
step value V, hence determine the current growth in the inductor due to the step
voltage V.
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THE HONG KONG POLYTECHNIC UNIVERSITY
Department of Electronic and Information Engineering
ENG237-E03r1
Discussion
1. In Figure 2, why RC = 5 MΩ and the charging voltage = 2.5 V? Can you use an
appropriate theorem to justify them?
2. Explain any differences between the experimental curves and the curves displayed on
the CRO.
3. Comment on the value of RC in (2) and the time taken (from the experiment curve) to
reach 63.2% of the total change.
4. Were the experimental results of (6) are expected. Explain.
5. Discuss the charge and discharge curves.
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