a practical exercise...capacitor transients 3 of 17 step three: firing transient determine the...

Capacitor Transients – Simulator Applet Updated 20 JUN 2019

A Practical Exercise Name:________________ Section: ____________

I. Purpose.

1. Review the operation of the oscilloscope.

2. Review the measurement of DC voltages using an oscilloscope.

3. Introduce the capture and display of an electrical signal with the oscilloscope.

4. Introduce the variation of voltage across a capacitor during charging and discharging.

II. Equipment.

Agilent E3620A Dual DC Power Supply

Oscilloscope

Relay and Trigger Box, Ink Pen, 12ft of 24 AWG wire, 15000-μF capacitor w/ discharge resistor

47Ω resistor

Safety Glasses

Circuit Simulator Applet

An introduction to the Circuit Simulator Applet

III. Pre-lab calculations. Show all work.

Step One: Determine the expected steady-state voltage VC across the capacitor in the circuit of Figure 1

when the switch is in position a (charging circuit is BOLD). Remember that capacitors act like an open

circuit under steady-state DC conditions.

DC DC

V124 V

V212 V

2 kΩ DischargeResistor

Coil Resistance0.3 Ω

+ -15,000 µF

PushbuttonTrigger

Relay Switch

47 ΩCurrent Limiting Resistor

b a

VC = _____

Figure 1

http://www.falstad.com/circuit/circuitjs.html

http://bait-consulting.com/publications/circuit_simulator_manual.pdf

Capacitor Transients

2 of 17

Step Two: Charging Transient

□ Determine the equation for the voltage across the capacitor while it is charging. Assume the

capacitor is initially discharged with the pushbutton trigger pressed closed. The transient will begin

when the pushbutton trigger is released and the relay switch moves to position a.

Hint: this is not the simple circuit first discussed in the lecture. You must find the Thèvenin equivalent

of the circuit, treating the capacitor as the load. The Thèvenin resistance will be used in calculating the

time constant.

vC (t)= __________________________

□ How long do you predict the charging transient will last?

t = ______________

□ Sketch the voltage across the capacitor during the charging transient. Label the axis for peak voltage

and time.


3 of 17

Step Three: Firing Transient

□ Determine the equation for the voltage across the capacitor while the coil gun is firing. Assume the

capacitor is initially fully charged with the switch in position a. The transient begins when the

trigger is pressed and the relay switches to position b (discharging circuit is BOLD). The inductance

of the coil is negligible when determining the discharge transient of this circuit. The coil can be

treated as a simple resistor of 0.3 ohms.

DC DC

V124 V

V212 V



+ -15,000 µF

PushbuttonTrigger

Relay Switch


ab

vC (t)= __________________________

□ How long do you predict the discharge transient will last?

t = ______________

□ Sketch the voltage across the capacitor during the discharge transient. Label the axis for peak

voltage and time.


4 of 17

Step Four: Discharge Transient

□ Determine the equation for the voltage across the capacitor while it is discharging. Assume the

capacitor is initially fully charged with the pushbutton trigger switch open. The transient begins

when the power source is turned off. Hint: when the power supply is turned off, it acts as an open

circuit.

DC DC

V124 V

V212 V



+ -15,000 µF

PushbuttonTrigger

Relay Switch


ab

vC (t)= __________________________


t = ______________


voltage and time.

Step Five: Instructor verification that pre-lab calculations are complete.

_____________________


5 of 17

IV. Lab Procedure. Time required: 60 minutes. Check-off each step as you complete it.

WARNINGS:

1. SAFETY GLASSES MUST BE WORN AT ALL TIMES. Violation will result in a 0 lab

grade for the term.

2. CAPACITORS HAVE DANGEROUS AMOUNTS OF ENERGY. FOLLOW ALL

PROCEDURES EXACTLY AND VERIFY ZERO VOLTAGE BEFORE TOUCHING.

Step One – INSTRUCTOR DEMONSTARION:

□ Ensure V1 and V2 of the power supply are both set to 0V. Turn off power supply.***

□ Wrap the ink pen barrel with the 24 AWG wire provided to construct your coil gun. You may add as

many layers of wire coils as you desire, but you must leave 1ft of wire on each end to plug into the

firing circuit. For best results, ensure the current is flowing the same direction in all the coils (i.e.

clockwise or counter clockwise) and that the coil begins directly in front of the loaded projectile as

shown below.


6 of 17

□ On your QUAD board, construct the coil gun circuit using Figures 3 and 4 below. Ensure that the

capacitor’s polarity is correct

***DO NOT TURN ON POWER SUPPLY UNTIL YOUR CIRCUIT HAS BEEN CHECKED.

DC DC

V1 V2

2 kΩ

+ -15,000 µF

1Trigger

A

4

7

Trigger and Relay Box

47 Ω

Figure 2

4

7

1

A

Figure 3

DMM

Volts


7 of 17

Step Two – INSTRUCTOR DEMONSTARION: Test fire coil gun

□ 24V Test Fire: Set V1 to 24V and V2 to 0V. Verify that the DMM reads ~ 24V. For safety, the

DMM provides constant monitoring of the capacitor voltage. DO NOT TOUCH THE

CAPACITOR WHILE THE DMM READS MORE THAN 500 mV.

□ With the projectile loaded and coil gun aimed in a safe direction, press the trigger to fire the

projectile. The projectile should only travel a few inches. If not, adjust the coil position by

sliding it up and down the pen until you get a successful launch.

□ 36V Test Fire: Set V1 to 24V and V2 to 12V. Verify that the DMM reads ~ 36V.


projectile. The projectile should travel a few feet. If needed, adjust the coil position for best

performance.

□ 48V Test Fire: Set V1 to 24V and V2 to 24V. Verify that the DMM reads ~48V.


projectile.

□ The equation for energy stored in a capacitor is below and is proportional to voltage squared.

Therefore, you should have observed an exponential increase of velocity and distance as the

voltage was increased.

Step three: Create Circuit in Simulation Applet

□ Build the following circuit. NOTE: The inductor is being modeled by a 0.3 Ohm resistor.

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24 VDC Source 12 VDC Source

Push Switch Relay Polarized 15000 µF Capacitor

0.3 Ohm Resistor When constructing the circuit,

PAY ATTENTION TO THE

NODES (where connections

occur). The nodes are

annotated by the white dot.

Just because a wire crosses

does not mean it’s connected.

Connections only occur at the

nodes.


8 of 17

Step Four: Capture a capacitor discharging while firing

□ Select “View in Scope” for the Polarized Capacitor

□ RUN simulation until the capacitor voltage reaches the steady state voltage calculated in step 1 of

the pre-lab.

□ In the Scope Properties, set the Scroll Speed to 2ms/div and set the Simulation Speed to about 2/3

red.

□ Click and hold the Push Button until the Capacitor has discharged for half the scope (about 2-3 sec)

and in RAPID succession STOP the simulation.

NOTE: If you do hold the Push button long enough or do not STOP the simulation quick enough and

need to recharge the capacitor to try again, you can charge the capacitor more quickly by changing the

Scroll Speed to 200ms/div and the Simulation Speed to fully red. Remember to reset the settings before

discharging the Capacitor.

□ Sketch the picture on the scope for the capacitor transient on Figure 4. (Hint: It should look similar

to the Firing Transient of the pre-lab.) Label the voltage at the start of the firing transient.


9 of 17

Time: _____ s/div

Figure 4

□ Count the divisions between the voltage when it is fully charged and when the capacitor reaches

fully discharged. NOTE: The fully discharged voltage is not 0V, but can be calculated using 5τ and

the vC (t) equation in Step Three of the pre-lab.

How much time did the capacitor take to fully discharge? _______________

How does the charge time compare to the values calculated in step 3 of the pre-lab?

Exact__________ Very close__________ Very Different_________

Step Five: Capture the capacitor recharging after firing

□ In the Scope Properties, set the Scroll Speed to 200ms/div and set the Simulation Speed to fully red.


10 of 17

□ Run the Simulation until the Capacitor has fully charged (about 30 - 35 sec) and in RAPID

succession STOP the simulation.


to the Charging Transient of the pre-lab.) Label the voltage at the end of the firing transient.

Time: _____ s/div

Figure 5

□ Count the divisions between the voltage when it is fully discharged and when the capacitor reaches

fully charged. NOTE: The fully charged voltage is not 35.17 V, but can be calculated using 5τ and

the vC (t) equation in Step Two of the pre-lab.

How much time did the capacitor take to fully charge? _______________



1


11 of 17

Step Six: Analyze your results

□ Run the Simulation and allow the capacitor to continue charging for 1 minute.

What is Maximum voltage that your capacitor charged to: ________________

How does this voltage compare to the value of VC calculated in step 1 of the pre-lab?


What is the minimum voltage that your capacitor discharged to? _______________

When the capacitor reached its maximum voltage, how much current should be flowing through the

capacitor? _______________________________________________________________________

When the capacitor reached its maximum voltage, how much energy is stored in the capacitor?

WC =______________

Step Seven: Circuit Submission

□ Save the circuit to your computer and submit the circuit text file to your instructor for lab credit.

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12 of 17

Practical Exercise Submission Form Name:________________ Section: _____

III. Pre-lab calculations. Show all work.

Step One: Determine the expected steady-state voltage VC across the capacitor in the circuit of Figure 1

when the switch is in position a (charging circuit is BOLD). Remember that capacitors act like an open

circuit under steady-state DC conditions.

DC DC

V124 V

V212 V



+ -15,000 µF

PushbuttonTrigger

Relay Switch


b a

VC = _____

Figure 1


13 of 17

Step Two: Charging Transient

□ Determine the equation for the voltage across the capacitor while it is charging. Assume the

capacitor is initially discharged with the pushbutton trigger pressed closed. The transient will begin

when the pushbutton trigger is released and the relay switch moves to position a.

Hint: this is not the simple circuit first discussed in the lecture. You must find the Thèvenin equivalent

of the circuit, treating the capacitor as the load. The Thèvenin resistance will be used in calculating the

time constant.

vC (t)= __________________________

□ How long do you predict the charging transient will last?

t = ______________

□ Sketch the voltage across the capacitor during the charging transient. Label the axis for peak voltage

and time.


14 of 17

Step Three: Firing Transient

□ Determine the equation for the voltage across the capacitor while the coil gun is firing. Assume the

capacitor is initially fully charged with the switch in position a. The transient begins when the

trigger is pressed and the relay switches to position b (discharging circuit is BOLD). The inductance

of the coil is negligible when determining the discharge transient of this circuit. The coil can be

treated as a simple resistor of 0.3 ohms.

DC DC

V124 V

V212 V



+ -15,000 µF

PushbuttonTrigger

Relay Switch


ab

vC (t)= __________________________


t = ______________


voltage and time.


15 of 17

Step Four: Discharge Transient

□ Determine the equation for the voltage across the capacitor while it is discharging. Assume the

capacitor is initially fully charged with the pushbutton trigger switch open. The transient begins

when the power source is turned off. Hint: when the power supply is turned off, it acts as an open

circuit.

DC DC

V124 V

V212 V



+ -15,000 µF

PushbuttonTrigger

Relay Switch


ab

vC (t)= __________________________


t = ______________


voltage and time.

Step Five: Instructor verification that pre-lab calculations are complete.

_____________________


16 of 17

IV. Lab Procedure.

Step Four: Capture a capacitor discharging while firing


to the Firing Transient of the pre-lab.) Label the voltage at the start of the firing transient.

Time: _____ s/div

Figure 4

□ Count the divisions between the voltage when it is fully charged and when the capacitor reaches

fully discharged. NOTE: The fully discharged voltage is not 0V, but can be calculated using 5τ and

the vC (t) equation in Step Three of the pre-lab.

How much time did the capacitor take to fully discharge? _______________



Step Five: Capture the capacitor recharging after firing


to the Charging Transient of the pre-lab.) Label the voltage at the end of the firing transient.

Time: _____ s/div

Figure 5

1

1


17 of 17

□ Count the divisions between the voltage when it is fully discharged and when the capacitor reaches

fully charged. NOTE: The fully charged voltage is not 35.17 V, but can be calculated using 5τ and

the vC (t) equation in Step Two of the pre-lab.

How much time did the capacitor take to fully charge? _______________



Step Six: Analyze your results

What is Maximum voltage that your capacitor charged to: ________________

How does this voltage compare to the value of VC calculated in step 1 of the pre-lab?


What is the minimum voltage that your capacitor discharged to? _______________

When the capacitor reached its maximum voltage, how much current should be flowing through the

capacitor? _______________________________________________________________________

When the capacitor reached its maximum voltage, how much energy is stored in the capacitor?

WC =______________

Step Seven: Circuit Submission

□ Save the circuit to your computer and submit the circuit text file to your instructor for lab credit.

21

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a practical exercise...capacitor transients 3 of 17 step three: firing transient determine the...

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