De Anza College Transient Time Behavior of Charging & Discharging of A Capacitor Lab Report

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Lab #7. AC circuit, oscilloscope, frequency, period, amplitude, Vpp, Vrms, AC-power For this lab we will use the simulation: or offline by using the HTML5 interactive simulation in the file: /circuit-construction-kit-ac_en.htm No fit analysis or official report for this lab. Answer only the questions. Purpose of this week’s lab: To study the transient time-behavior of the charging and discharging of a capacitor and to compare this behavior to a circuit with a coil. Use a simulated oscilloscope to measure the parameters of signals: frequency, period, amplitude, Vpp, Vrms, and AC-power Part I The RC circuit To understand the equipment represented here, look up the theory in your textbook. Process 1: Watch the demo video of the charge of the capacitor: Cap_charge-discharge-demo.mp4 Notice that the circuit is the same as in the lab manual of Lab 7. The light bulbs show the current flow through the circuit and the “light rays” indicate the intensity. Therefore, by looking at them you can see what happens in the simulated circuit. Also, the Voltage plot shows the voltage across the capacitor when it is empty 0 Volts and when it is fully charged at 25 Volts. Observe the behavior of the 2 light bulbs when either of the 2 switch is closed. Initially observe what will happen when the switch A closes, and the capacitor is charged from the battery. Then observe what happens when the switch A opens, and the switch B closes, and the capacitor is discharged through the resistor R =10 Ohm. Q1: describe in a short paragraph the progression of the light intensity versus the voltage drop across the capacitor that you can see on the Voltage-vs-Time plot. Process 2: Observe the timer of the simulation. Notice the time it takes for the light bulbs to go from full shine to zero during the charge and discharge steps of the simulation. Notice that the charge takes longer (in my simulation 24±1 s) than the discharge (in my simulation 12±1 s). Remember from the theory that total charge or discharge happens at least 3* seconds from the moment of the closing or opening a switch, and the  is the characteristic time constant. Then we can conclude that the charge and discharge circuits (as they are created by the opening and closing of the 2 switches) have different time characteristics. Q2: investigate around the circuit to find why. Remember that the characteristic is R*C value. Write a paragraph explaining your findings. Q3: if you find the 2 different time characteristics of the 2 circuit versions (charge-discharge) then calculate if the 3* for each one justifies the time it takes for the bulbs to turn off. Write a short paragraph explaining how close to the expected numbers (from my simulation) your calculations lie. Part II the RL circuit Process 3: watch the demo video: DC_Bulb_onoff.mp4. It shows the normal, DC behavior of the light bulb with an on/off switch and a resistor in series with a battery. Observe the shape of the voltage vs. time on the virtual voltage chart. It is the usual, expected square shape of on/off between 0 and 4 Volts. It is very basic. Nothing to write about. Now watch the demo video: DC_Bulb_n_Coil_onoff.mp4. This one is the same circuit as before with the addition of the branch with the coil by the closing the switch in series with it. Now the light bulb is in parallel to the coil. When the switch controlling the battery is turned on or off the shape of the voltage in the chart and the light intensity of the bulbs is different from the previous demo video. I made these demo’s separate so you can observe them at the same time if you need. Q4: Write a paragraph explaining why this is happening. Try to look in your textbook under Lenz’s law. Describe how it applies here. Q5: Bonus-Optional. Try to estimate a characteristic time for the circuit. Use the video player time to measure how long it took the voltage across the light bulb to go from the max to almost zero. Part III Vpp, Vrms and power. Process 4: Read from the oscilloscope. For this part we will use the demo applet: bring the parameters of the two simulated signals according to the picture. The Oscilloscope is a tool that you will use throughout your career with analog or digital signals. The physical instrument operations and assistive capabilities will vary with the investment level or the evolution of the tech. The measurement that you will perform have not changed since the time of its inception and will not change in the future. Physical instrument or simulation applet there are only 3 direct measurements that one can make: Vpp*, period, and phase. That is because you have 2 dimensions, so you can measure voltage difference and time difference. All others are secondary or assistive measurements like the amplitude or Vrms. *(if you do not remember what is Vpp, see here: The reason for these particular primary measurements is that one can only measure “the position of features” in the 2-D grid of time-voltage of the oscilloscope screen. That is why measuring Vpp (= 2 * Vamplitude) is better than trying to measure Vamplitude directly. Where could you place the volts = 0.0 V of a sine wave for the switch from positive to negative values? How would you even choose the “zero-level” for a generic wave form that is not symmetric around the time axis? Q6: Based on the discussion of amplitude measurement above discuss how one should choose how to measure the frequency or period? Can you use the same thinking to measure phase differences? Q7: Verify your answer of Q6, by “measuring” the Vpp and period of both the sine waves, as well as the phase difference between them. Use the scales of the applet to verify the values. How close to these values can you get? (i.e. What is the size of uncertainty? ..and its source of course?). Challenge process (optional): Power For this challenge we will use Set the only control “phase” of the waveforms of voltage V(t) and current I(t) to a random value of phase difference of your choice. Measure on the screen or from the indicators the values of the instantaneous voltage and current. Estimate the power use on the simulated component at time t=4.0 sec, chose a value of time for which the green form is not too close to 0.0 Joules. Challenge question: How close to the value you can read from the screen is the estimated instantaneous power value? Can you estimate the average power spend on this simulated component?
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Explanation & Answer

Hi please check the attached file,

When switch A closes (B remain open), the light intensity is highest and voltage drop is 0, then the
voltage drop across the capacitor increases and the line intensity decreases. When the voltage drop
reach 25 V, the light intensity of both light bulb becomes 0. When B close and (A open), 20 ohm bulb
has no light, the light intensity of 10 ohm bulb is highest and the voltage cross capacitor is the largest at
the switch close. As the voltage drop across the capacitor decreases gradually, the light intensity also

When A closes B opens the two light bulbs and 10 ohm resistor are in series with the capacitor, the total
resistance of the circuit is 40 ohms. When A opens and B closes, only 10ohm resistor and 10ohm bulb
in series with the capacitor, the resistance of the circuit is 20 ohms. The time constant of RC circuit is RC.
This explains why it takes longer to charge the capacitor than discharge the capacitor.

As A closes, the time constant of the circuit in this case is
=RC = 40*0.2 = 8 s
The charging time is about 3=3*8 s = 24 s
This result is very close to to the simulation result of 241 s.
As B closes, the time constant of the circuit in this case is
=RC = 20*0.2 = 4 s
The charging time is 3=3*4 =12 s.
This result matches very well with the simulation result of 121 s.

For the circuit without the coil, when the switch is on, the light bulb goes bright almost immediately, and
it dim qui...

Really useful study material!

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