## (solution) ELEC153 Circuit Theory II M1A3 Lab: C and L Circuits Transient

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ELEC153 Circuit Theory II

M1A3 Lab: C and L Circuits Transient Analysis

Introduction

Before we get into the ?real? AC circuits, this very first lab is about transient analysis for RC and

RL circuits. We will investigate the transient properties of RC and RL circuits.

Procedure

1. Setup the following RC circuit in MultiSim. The voltage source is 12 V DC: Fig. 1. RC circuit transient analysis

2. Select ?simulate ? Analysis ? Transient Analysis? from the MultiSim Menu, the following

window appears: Fig. 2. Parameter settings

Select the ?Analysis parameters? as shown above and the ?Output? as shown below: Fig. 3. Output selection

3. Click ?Simulate? from the above window, you will see the following transient response: Fig. 4. Transient response of RC circuit

The ?Design1? title will automatically change once you change your file name. You can see that

since the initial capacitor voltage is 0 V and the voltage cannot be changed instantaneously, it

takes about 5 ms for it to reach 12 V (at which point the capacitor is like an open circuit and

there is no current flowing so the voltage drop on the resistor is 0 V). This is called the steady

state. The time constant, which is equal to RC, is a measure of how fast the RC circuit can reach

its steady state. An RC circuit with zero initial condition will need about 5 time constants (page

416 in textbook) to reach its steady state. In this setup, RC=1K*1uF=1000*0.001ms =1ms. So 5

ms is the time to reach the steady state, as confirm by the above figure.

Task 1: Change R1 in Fig. 1 to 2K? and keep C1 the same, perform the simulation, measure

the time constant and compare it to the calculated one. Do the same for R1=2K? and C1=0.5

uF.

4. Change the capacitor in Fig. 1 to an inductor, as shown in Fig. 5. Keep the simulation

parameters the same and change output to I(L1) (make sure you remove V(2)). Perform the

simulation and the RL transient response will appear (Fig. 6). Fig. 5. Circuit for RL transient analysis Fig. 6. Transient response of RL circuit

Again, you can see that since the initial inductor current is 0 A and the current cannot be changed

instantaneously, it takes about 5 ms for it to reach 12 mA (at which point the inductor is like a

short circuit and the circuit current is simply the maximum of 12V/1K? =12 mA). This is called

the steady state. The time constant, which is equal to L/R, is a measure of how fast the RL circuit

can reach its steady state. An RL circuit with zero initial condition will need about 5 time

constants (page 476 in textbook) to reach its steady state. In this setup, L/R = 1/1000 = 1ms. So

5ms is the time to reach the steady state, as confirmed by the above figure. Task 2: Change R1 in Fig. 5 to 2 K? and keep L1 the same, perform the simulation, measure the

time constant and compare it to the calculated one. Do the same for R1=2 K? and L1=2 H.

In general, for each lab you do, you will be asked to setup certain circuits, simulate them, record

the results, verify the results are correct by hand, and then discuss the solution. Your lab write-up

should contain a one page, single spaced discussion of the lab experiment, what went right for

you, what you had difficulty with, what you learned from the experiment, how it applies to our

coursework, and any other comment you can think of. In addition, you should include screen

shots from the MultiSim software and any other figures, tables, or diagrams as necessary.

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