RL & RLC Circuits

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German – Jordanian University (GJU)

Electrical Circuits 1 Laboratory

Section 3

Experiment 8 RL & RLC Circuits

Post lab Report

Mahmood Hisham Shubbak

Student number: 12

21 / 12 / 2008

Objectives:

9 To learn about the behavior of series RL and RLC circuits.

Introduction and Theory:

An Inductor is a device consists of a coil of conducting wire, and it is designed to store energy in its magnetic field.

The Inductance of an Inductor is the property whereby an inductor exhibits opposition to the change of current flowing through it, measured in henrys (H).

Where: v: the voltage drop across the Inductor. L: the Inductance. i: the current flowing through the Inductor.

L1 47mH

‐ An Inductor –

The current in an inductor doesn’t change instantaneously.

The energy stored in an Inductor is given by: 1 2

We can combine Inductors in two ways:

1. In series: ‐ We can replace all the Inductors with an equivalent Inductor whose Inductance is given by:

L ‐ Inductors in series are like Resistors in series.

2. In parallel: ‐ We can replace all the Inductors with an equivalent Inductor whose Inductance is given by:

N 1 1 ‐ Inductors in Parallel are like Resistors in Parallel.

The Response of an RL circuit is given by the following equation: Where:

The Response of an RLC circuit is described by the following equations:

In Series In Parallel α ⁄ ⁄ Ωo ⁄√ ⁄√

We assume: y(t) ≡ I or V

y final ≡ y steady state ,

1. [ If ] Then the Circuit's Response is Overdamped.

2. [ If ] Then the Circuit's Response is Critically damped. [Here S1=S2=S= ‐ α]

3. [ If ] Then the Circuit's Response is Underdamped. [Here S1, S2 are complex numbers = ‐α ± j = a + jb ]

9 This experiment consists of three parts:

Part A:

Procedure:

1. Measure the internal resistance of the inductor. 2. Connect the circuit in the figure below.

1 L1 2 10mH

Vdc R1 5 V 1kΩ

3. Measure VL and VR for the circuit. 4. Measure the current of the circuit I. 5. Compare the experimental values with the calculated. 6. Why was there a non‐zero voltage across the two terminals of the Inductor?

Results:

1. RL = 53.3 Ω

‐ The simulation results of this part are shown in the figure below:

V: 5.00 V V: 5.00 V 12 I: 5.00 mA L1 I: 5.00 mA 10mH

Vdc R1 5 V 1kΩ

V: 0 V 0 I: 5.00 mA

‐ The experimental results of this part are shown in the table below:

Simulation Experimental

VL 0 V 0.44 V VR 5 V 4.56 V I 5 mA 4.7 mA

9 The Reason behind the non‐zero voltage across the two terminals of the Inductor is its internal resistance (in this case our inductor like a connection of an inductor 10mH with 53.3Ω Resistor in series). V I RRL

Part B:

Procedure:

1. Measure the internal resistance of the inductor. 2. Connect the circuit in the figure below. 1 L1 10mH

Square wave XFG1 250 Hz CH1 2Vpp 1V DC offset R 220Ω 0, GND

3. Connect the CH1 and GND of the oscilloscope as shown.

4. Draw the VR then find IL.

Results:

‐ The internal Resistance of the Inductor RL = 53.3 Ω.

‐ The result graphs of this part are shown in the last page of this report.

‐ We can get the IL graph by dividing VR by (R+RL) as: IVR⁄R RL

Part C:

Procedure:

1. Connect the circuit in the figure below. C1 2 L1 10mH 1 2.2uF Square wave XFG1 100 Hz CH1 2Vpp 1V DC offset R 390Ω 0, GND

2. Connect the CH1 and GND of the oscilloscope as shown.

3. Draw the VR then find IL.

4. Calculate α and ωo ,what kind of response does the circuit exhibit?

Results:

The graphs of this part are drawn on the last page.

This circuit is series RLC circuit, i.e. ⁄ 390⁄ 2 102 19500

2 6 ⁄ 1⁄ 10 2.210 45454545. 45 .

Then the Circuit's Response is Overdamped.

Discussion:

Part A is a basic RL circuit with dc source, L acts as a short circuit.

The difference between the theoretical and experimental results is due to the internal resistance of the inductor which was = 53.3Ω

V I 4.7mA RRL .

Part B is also a basic RL circuit but with Ac source.

The difference between the theoretical and experimental results is due to the internal resistance of the inductor which was = 53.3Ω

IVR⁄R RL

IVR⁄1053.3Ω

We had the voltage drop across R with Vpp=1.16V

We notice that the Inductor smooths the voltage.

Part C represents an over damped RLC circuit with Ac source.

The difference between the theoretical and experimental results is due to the internal resistance of the inductor which was = 53.3Ω

We had the voltage drop across R with Vpp=2.62V

Conclusion

9 Inductors in series act like resistors and it is given by: Le = Σ Li

9 Inductors in parallel act like resistors and it is given by: 1/Le = Σ 1/Li

9 The Inductances energy is given by: 1 2

9 LC circuit response is given by:

9 Time constant τ = L/R

9 The response of RLC circuit is given by a 2nd order differential equation and it can be over damped, critically damped or underdamped.

9 An Inductor in the steady state (after a long time) reacts as a short circuit.