1
Basic RL and RC DC Circuits
Objective
In this exercise, the DC steady state response of simple RL and RC circuits is examined. The transient
behavior of RC circuits is also tested.
Theory Overview
The DC steady state response of RL and RC circuits are essential opposite of each other: that is, once steady
state is reached, capacitors behave as open circuits while inductors behave as short circuits. In practicality,
steady state is reached after five time constants. The time constant for an RC circuit is simply the effective
capacitance times the effective resistance, τ = RC. In the inductive case, the time constant is the effective
inductance divided by the effective resistance, τ = L/R.
Equipment
(1) DC power supply
(1) DMM
(1) Stop watch
model:________________ srn:__________________
model:________________ srn:__________________
Components
(1) 1 µF
(1) 470 µF
(1) 10 mH
actual:__________________
actual:__________________
actual:__________________
(1) 10 k
actual:__________________
(1) 47 k
actual:__________________
Schematics
Figure 1.1
Figure 1.2
Procedure
RL Circuit
1. Using figure 1.1 with E=10 V, R=47 k, and L=10 mH, calculate the time constant and record it in
Table 1.1. Also, calculate and record the expected steady state inductor voltage in Table 1.2.
2. Set the power supply to 10 V but do not hook it up to the remainder of the circuit. After connecting
the resistor and inductor, connect the DMM across the inductor set to read DC voltage (20 volt scale).
3. Connect the power supply to the circuit. The circuit should reach steady state very quickly, in much
less than one second. Record the experimental inductor voltage in Table 1.2. Also, compute and
record the percent deviation between experimental and theory in Table 1.2.
RC Circuit
4. Using figure 1.2 with E=10 V, R1=47 k, R2=10k and C=1 µF, calculate the time constant and
record it in Table 1.3. Also, calculate and record the expected steady state capacitor voltage in Table
1.4.
5. Set the power supply to 10 V but do not hook it up to the remainder of the circuit. After connecting
the resistors and capacitor, connect the DMM across the capacitor set to read DC voltage (20 volt
scale).
6. Connect the power supply to the circuit. The circuit should reach steady state quickly, in under one
second. Record the experimental capacitor voltage in Table 1.4. Also, compute and record the percent
deviation between experimental and theory in Table 1.4.
RC Circuit (long time constant)
7. Using figure 1.2 with E=10 V, R1=47k, R2=10 k and C=470 µF, calculate the time constant and
record it in Table 1.5. Also, calculate and record the expected steady state capacitor voltage in Table
1.5.
8. Set the power supply to standby, and after waiting a moment for the capacitor to discharge, remove
the capacitor and replace it with the 470 µF. Connect the DMM across the capacitor set to read DC
voltage (20 volt scale).
9. Energize the circuit and record the capacitor voltage every 10 seconds as shown in Table 1.6. This is
the charge phase.
10. Remove the power supply from the circuit and record the capacitor voltage every 10 seconds as
shown in Table 1.7. This is the discharge phase.
11. Using the data from Tables 1.6 and 1.7, create two plots of capacitor voltage versus time and compare
them to the theoretical plots found in the text.
Data Tables
τ
212.77 ns
Table 1.1
VL Theory
VL Experimental
Deviation
9.45 mV
9.48 mV
0V
Table 1.2
8.24ms
τ
Table 1.3
VC Theory
VC Experimental
Deviation
23.85 mV
23.87mV
0V
Table 1.4
3.88ms
τ
50.78 uV
VC Theory
Table 1.5
Time (sec)
Voltage
0
10
20
30
40
50
60
70
80
90
100
110
120
Table 1.6
Time (sec)
Voltage
0
10
20
30
40
50
60
70
80
90
100
110
120
Table 1.7
Questions
1. What is a reasonable approximation for an inductor at DC steady state?
An inductor at a DC Steady State is the one that stores energy in the magnetic field and also they return
energy to the circuit whenever it is required to do so. Therefore, it is said that the larger the resistance, the
smaller the time constant, the faster the inductor would store and decay energy. For me, the reasonable
approximation for an inductor at DC steady state, solely depends on the resistance and the time constant
of the circuit. Therefore, the inductors act as short circuits during DC Steady State.
2. What is a reasonable approximation for a capacitor at DC steady state?
A capacitor at a DC Steady State has the ability to store energy in the form of an electrical charge
producing a potential difference. Therefore, it charges up to its supply voltage but blocks the flow of
current through it is because the dielectric of a capacitor doesn’t conduct electric flow in the circuit. So
basically the capacitor act like open circuits during in DC steady state. Therefore, is no reasonable
approximation of a capacitor at DC Steady State.
3. How can a reasonable approximation for time-to-steady state of an RC circuit be computed?
I therefore conclude that the approximation for time to steady state of an RC Circuit can be computed by
5 time constants t=5t=5RC, VC=E(1-e^(-t/T)), where E is the voltage source and T is the time constant. It
depends on the value of the voltage source and the time constant so you will be able to see a reasonable
approximation of it.
4. In general, what sorts of shapes do the charge and discharge voltages of DC RC circuits follow?
In general, and RC Circuit obviously have a resistor and a capacitor when connected to a DC voltage
source. While charging, the capacitor is initially discharged, but as soon as the switch was close the
current flows through it. And as it increases, there will be an increasing opposition to the flow of charge
by the repulsion of like charges on each plate.
Moreover, while discharging, as the voltage decreases, the current and the rate of discharge decreases.