İzmir Katip Çelebi University

Faculty of Engineering and Architecture

Department of Electrical and Electronics Engineering
Student Name Mert Can Uludağ
Student Number 210403060
Submission Date 29.05.24
Group Number 23

EEE204 Electronics Laboratory

Lab Report

Introduction to RL and RC Circuits

Abstract Section

The principal objective of this experiment was to investigate the DC steady-state and
transient behavior of RL and RC circuits. Specifically, the experiment aimed to measure and
compare theoretical and experimental values of time constants and voltage responses in both
types of circuits. The methods employed included assembling RL and RC circuits as per the
provided schematics, utilizing a DC power supply and a digital multimeter (DMM) to
measure voltage, and using a stopwatch to record transient responses. For the RL circuit, with
a resistor (R=47 kΩ) and inductor (L=10 mH), the time constant was calculated and the
steady-state inductor voltage was recorded. For the RC circuits, two configurations were
tested: one with a capacitor (C=1 µF) and another with a larger capacitor (C=470 µF) in series
with resistors (R1=47 kΩ, R2=10 kΩ). The time constants and steady-state capacitor voltages
were determined for both configurations, with the transient response recorded for the larger
capacitor.
Quantitative results showed that for the RL circuit, the calculated time constant was τ =
L/R = 0.21 ms. The experimental steady-state inductor voltage closely matched the theoretical
value, with minor deviations attributed to experimental error. For the RC circuit with C=1 µF,
the time constant was τ = RC = 47 ms, and the experimental steady-state capacitor voltage
aligned with theoretical predictions. The RC circuit with C=470 µF had a significantly larger
time constant, τ = 22.1 seconds, and the voltage measurements during charging and
discharging phases provided data points every 10 seconds that closely followed the theoretical
exponential curves.

In conclusion, the experimental results confirmed the theoretical expectations for both RL
and RC circuits in DC steady-state and transient conditions. The capacitors behaved as open
circuits and inductors as short circuits in steady-state, as predicted. The transient responses of
the RC circuit, particularly with the larger capacitor, demonstrated the expected exponential
charging and discharging behavior. Minor discrepancies between experimental and theoretical
values were within acceptable ranges, validating the accuracy of the experimental setup and
methods. This experiment reinforces the fundamental concepts of time constants and steady-
state behavior in RL and RC circuits.
Introduction Section:
The primary goal of this experiment is to examine the DC steady-state and transient
behaviors of RL and RC circuits. By understanding these behaviors, we can predict how
inductors and capacitors react in electrical circuits, which is crucial for designing and
analyzing a wide range of electronic systems.

This experiment is significant because it demonstrates the fundamental principles of electrical

circuits in practical scenarios. Capacitors and inductors are essential components in many
electronic devices, from simple filters to complex communication systems. Understanding
their behavior in steady-state and transient conditions allows engineers to design circuits with
desired characteristics and stability.

The experiment involves calculating time constants and measuring voltage responses in RL
and RC circuits. For the RL circuit, we will use a resistor and inductor to determine the time
constant and steady-state inductor voltage. For the RC circuits, we will investigate two
configurations: one with a small capacitor and another with a larger capacitor, both in series
with resistors. The time constants and steady-state voltages will be calculated and compared
with experimental measurements.

By systematically recording and analyzing these values, we gain insights into the transient
and steady-state responses of RL and RC circuits, reinforcing theoretical concepts with
practical observations. This understanding is essential for the effective design and
troubleshooting of electronic circuits in various applications.

Experimental Procedure Section:

The experiment examined the DC steady-state and transient behavior of RL and RC circuits,
based on the principles that inductors act as short circuits and capacitors as open circuits at
L
steady state. The time constants for RL and RC circuits are τ = and τ =R ×C respectively.
R

Instruments and Components:

- DC power supply, Digital Multimeter (DMM), Stopwatch, Resistors: 10 kΩ and 47

kΩ, , ,Inductor: 10 mH, Capacitors: 1 µF and 470 µF

Procedures:

1. RL Circuit:
 - Setup: Assemble a circuit with a 47 kΩ resistor and a 10 mH inductor in series. Connect to
a 10 V DC power supply.

L
- Calculation: Compute the time constant τ =
R

- Measurement: Connect the DMM across the inductor to measure the steady-state voltage
after energizing the circuit.

2. RC Circuit (1 µF):

- Setup: Assemble a circuit with a 47 kΩ resistor and a 1 µF capacitor in series. Connect to a

10 V DC power supply.

- Calculation: Compute the time constant τ =R ×C

- Measurement: Connect the DMM across the capacitor to measure the steady-state voltage
after energizing the circuit.

3. RC Circuit (470 µF):

- Setup: Assemble a circuit with a 47 kΩ and a 10 kΩ resistor in series with a 470 µF

capacitor. Connect to a 10 V DC power supply.

- Calculation: Compute the time constant τ =R ×C

- Charge Phase: Measure the voltage across the capacitor every 10 seconds during charging.

- Discharge Phase: Disconnect the power supply and measure the voltage across the
capacitor every 10 seconds during discharging.

Results and Discussion Section:

Results

The results of the experiment demonstrated the expected behaviors of RL and RC circuits in
both DC steady-state and transient conditions. The theoretical and experimental values were
compared to validate our understanding.

RL Circuit:

- Theoretical Calculation:
 L 10 mH
- Time constant: τ = = = 0.21 ms
R 47 kohm

- Steady-state inductor voltage: Expected to be 0 V as the inductor behaves as a short circuit.

- Experimental Results:

- Steady-state inductor voltage: 0 V

- The experimental results matched the theoretical prediction, confirming the inductor’s
behavior in steady-state.

RC Circuit (1 µF):

- Theoretical Calculation:

- Time constant: τ =RTh×C =8.24 kohm×1 uF=8.24 ms

- Steady-state capacitor voltage: Expected to be 10 V as the capacitor behaves as an open

circuit.

-Experimental Results:

- Steady-state capacitor voltage: 10 V

 - The experimental data was in close agreement with the theoretical values, verifying the
open-circuit behavior of the capacitor.

Analysis:

The voltage data during both the charging and discharging phases closely followed the
theoretical exponential curves, confirming the expected transient behavior of the RC circuit.

Conclusion:

The experimental results validated the theoretical predictions for both RL and RC circuits. In
the steady-state, the inductor acted as a short circuit and the capacitor as an open circuit.
During the transient response, the RC circuit displayed exponential charging and discharging
behaviors consistent with calculated time constants. Minor deviations between theoretical and
experimental values were within acceptable error margins, affirming the accuracy of the
experimental setup and reinforcing the fundamental principles of circuit analysis.

0.21×10−6
τ
Table 1.1
 VL Theory VL Experimental Deviation
0V 0V 0V

Table 1.2

8.2×10−3
τ
Table 1.3

VC Theory VC Experimental Deviation

10V 10V 0

Table 1.4

3.88
τ charge
26.79
τ discharge
10V
VC Theory

Table 1.5

Time (sec) Voltage

0V
0

3.05V
10
6V
20
7.26V
30

8.07V
40

8.95V
50
9.26V
60
9.43V
70

9.72V
80
 9.83V
90

9.84V
100

9.95V
110

10.01V
120

Table 1.6
Time (sec) Voltage

9.95V
0

5.6V
10

3.8V
20

2.7V
30

1.6V
40

1.3V
50

1.1V
60

0.77V
70

0.43V
80

0.22V
90

0.26V
100

0.12V
110

0.08V
120

0.06V
130

0.04V
140

0.03V
150

Table 1.7
Conclusion Section
Tasks:
1. Measure the DC steady-state response of an RL circuit.
2. Measure the DC steady-state response of an RC circuit with a small capacitance (1 µF).
3. Measure the transient response of an RC circuit with a larger capacitance (470 µF) during
both the charge and discharge phases.

Conclusions:

1. RL Circuit:
- Task: Measure the DC steady-state response.
- Conclusion: The RL circuit reached steady state very quickly, with the inductor behaving
as a short circuit, resulting in an inductor voltage of 0 V at steady state. This matched the
theoretical prediction.

2. RC Circuit (1 µF):
- Task: Measure the DC steady-state response.
- Conclusion: The RC circuit with a 1 µF capacitor behaved as an open circuit at steady
state, with the capacitor voltage reaching 10 V, in line with the theoretical expectation.

3. RC Circuit (470 µF):

- Task: Measure the transient response during charge and discharge phases.
- Conclusion: The RC circuit exhibited an exponential charging and discharging behavior as
predicted. The time constant was calculated to be 3.87 seconds, and the experimental data
closely followed the theoretical exponential curves.
Recommendations:

1. For Future Experiments:

- Ensure that all components are within their specified tolerance ranges to minimize
deviations between theoretical and experimental results.
- Use an oscilloscope for more precise measurement of transient behaviors, especially for
capturing rapid changes in voltage.

2. For Practical Applications:

- When designing circuits that require specific time constants, accurately calculate the
combined resistance for parallel and series configurations to achieve desired performance.
- Consider component tolerances and real-world deviations when designing circuits that rely
on precise time constants for critical applications.

These conclusions and recommendations provide a deeper understanding of the behavior of

RL and RC circuits, affirming the theoretical principles and guiding future experimental and
practical work in circuit design and analysis.

Questions

1. What is a reasonable approximation for an inductor at DC steady state?

A reasonable approximation for an inductor at DC steady state is that it behaves as a short
circuit. Therefore, the voltage across the inductor is effectively zero once steady state is
reached.

2. What is a reasonable approximation for a capacitor at DC steady state?

A reasonable approximation for a capacitor at DC steady state is that it behaves as
an open circuit. Therefore, the current through the capacitor is effectively zero once
steady state is reached.

3. How can a reasonable approximation for time-to-steady state of an RC circuit be

computed?
A reasonable approximation for the time-to-steady state of an RC circuit can be
computed using the time constant (τ). The time constant (τ) is the product of the
resistance (R) and the capacitance (C) in the circuit. Therefore, τ=RC. The time constant
represents the time it takes for the voltage or current to reach approximately 63.2% of its
final value during charging or discharging, respectively. Steady state is typically reached
after five time constants.
4. In general, what sorts of shapes do the charge and discharge voltages of DC RC circuits
follow?
The charge and discharge voltages of DC RC circuits typically follow exponential
curves. During charging, the voltage across the capacitor increases exponentially towards
the source voltage. During discharging, the voltage decreases exponentially towards zero.
−t
These curves can be described by the equation V(t)= V 0 ×(1−e RC ) , where V(t) is the
voltage across the capacitor at time t, V 0 is the initial voltage (source voltage during
charging or initial capacitor voltage during discharging),R is the resistance,C is the
capacitance, and τ=RC is the time constant of the circuit.