L lang="en">RC Time Constant
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Measurement that the Time constant in one RC Circuit
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In this rap experiment we will measure the time continuous τ of an RC circuit via three various methods. In number 1 we"ve sketched a collection RC circuit.
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Figure 1 - chart of an RC CircuitWhen the move is in position 1, the voltage resource supplies a present to the resistor and also the capacitor. Charge is deposit on the plates of the capacitor. At very first there is very little charge on the plates, however, together time walk on the charge on the plates builds up and the increased voltage throughout the capacitor will minimize the flow of existing through the circuit. We deserve to see this in the following loop equation:Vo + Vr + Vc = 0orVo - iR - q/C = 0As q gets larger, ns must obtain smaller to compensate. As time goes on, the currentwill eventually technique zero. When the move is moved to place 2, the battery is eliminated fromthe circuit, and the charge that has accumulated in the capacitor flows through the resistor. In this situation the equation is:iR + q/C = 0ordq/dt R + q/C = 0This an initial order differential equation has actually a systems in the type of an exponential:q(t) = qo e(- t / τ)Where τ = RC. This decaying role is plotted in figure 2:
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Figure 2 - Exponential DecayGiven the worths of R and also C in most circuits, it is really hard to "watch" the decay. In this rap we will certainly cheat a little bit, we will affix our RC circuit not to a voltage supply v a switch, however to a role generator that is outputting a square wave. This will act as an "on" and also "off" voltage supply hundreds or countless times per second. We can then observe the voltage across the circuit on one oscilloscope, and also measure τ from there.

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Procedure:Using her oscilloscope, measure the square-wave output from the role generator. Set the peak-to-peak voltage to at least ten volts and also position the waveform on the oscilloscope screenin a way that it is simple to measure up voltages. Together you perform this, likewise verify that the duration measuredon your oscilloscope is what girlfriend would intend from the frequency indigenous the function generator. Acommon mistake in this lab is to use an uncalibrated timescale.On your breadboard affix a capacitor and also resistor in series. Choose a pair v an RC the 10-4 secs or smaller. Note but that if you pick a capacitor through a very small capacitance, then the capacitanceof the rest of the circuit will dominate your measure up of τ. If your results for technique number#1 disagree strongly with techniques #2 and #3, climate you have actually ignored the warning about picking a an extremely smallcapacitance.Method #1 The an initial way to measure up the τ is to check out R & C directly off that the materials themselves. Since capacitorstypically have actually uncertainties of ± 20%, what is the uncertainty linked with this measurement?Method #2Connect her oscilloscope to measure the voltage across the capacitor. See figure 3. Note that the capacitorshould connect to ground, no the resistor. Think about this detail when friend make your measurements. If youmeasure incorrectly, you have the right to ground both political parties of the capacitor, in impact removing it from the circuit.
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Figure 3 - picture of RC CircuitOn your scope inspect the voltage across the capacitor. It should look something like figure 4. Note what may have actually to readjust the triggering on her oscilloscope.
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Figure 4 - Top: diagram of Voltage an answer Bottom: Voltage throughout the Capacitor ~ above the OscilloscopeExtend the duration of the role generator so that it looks choose the capacitor is totally discharging. "Blow up" this section of the graph by changing the time scale, this means you can check it an ext closely. See figure 5.
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Figure 5 - "Blow Up" the the decaying component of the waveformOur second an approach of measuring the time constant will it is in a "one point" measurement. Since e-1 = 0.368, take it the difference in between the highest and also lowest voltages, multiply this by 0.368, and add it to the lowestvoltage. Thatwill be the voltage across the capacitor after ~ one τ. Uncover this voltage level on your screen and also measure exactly how long it took forthe voltage throughout the capacitor to decay to this value. Together voltage coincides to one τ worth of decay, the isa straight measurement of τ. Psychic to include an calculation of error in your notebook. Calculation the error the very same wayyou would estimate the measure up error made once using a ruler.

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Method #3The final method of measuring τ is to take it data at many points. Exploit the truth that us havedigital oscilloscopes by saving the data on to a USB storage stick and also importing the data into Excel.If you then calculation a tower that is the organic log (ln) of her voltage, you can graph these data against time and also get an estimate for τ (actually, -1/τ). Usage the computer systems in lab come getthe slope and the error on the slope. Be conscious that few of your data are much more valuable 보다 others,and delete clues that room going to throw off her curve (think about the loved one error of part points compared to others).In your conclusion talk about the RC circuit, compare your values for τ v their uncertainties, and include your thoughts ~ above the best way to measure τ. Keep in mind that friend conclusion must be decently longer than persons you have written so much for this class, and that if your discussion does not incorporate comments ~ above the uncertainties in yourmeasurements, it will not be considered complete.