Physics 241 Lab: RC Circuits â AC Source

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1.2. The Source Voltage Equation: V source(t) V sourcesin( Dt )amplitudeThe source voltage equation is straightforward. It oscillates sinusoidally, i.e. it is a sine functionof time. The maximum voltage applied across the whole circuit is V source. The source oscillates with anamplitudeangular driving frequency D 2f D(which you will set later with your function generator). The sourcevoltage is phase shifted from the resistor voltage by an amount arctan C where X C is the reactive R capacitance of the capacitor given by the equation C 1 (more on this later). Note that this x-like DCvariables are really the capital Greek letter Chi (pronounced kai).If you look at the equation for resistor voltage, you will see no phase shift. Again, what thismeans is that we measure all phases in relation to the resistor not the source. The resistor will have itsmaximum voltage at a different time than when the source voltage is maximum.Imagine a sinusoidally driven RC circuit. If the source voltage has an amplitude ofV sourceamplitude=1.8 volts, a linear driving frequency f D =555 Hz, a resistance R=150 , and a capacitance C=1.5x10 -5 F,find the phase shift of the source voltage compared to the resistor. Your work and answer:1.3. The Resistor Voltage Equation: V R(t) R VZsourcesin( Dt)amplitudeThe resistor voltage oscillates sinusoidally without a phase shift while R is simply the resistance.Z is the impedance of the whole circuit. Z acts like the “total resistance” of the circuit. Z is measured inSI units of Ohms and is given by the equation Z R 2 L C 2 .This definition has new stuff, too. X L and X C are like the “resistances” of the inductor andcapacitor, respectively. We won’t study inductors until later in the semester, but it is easier to memorizethe complete equation. Since we don’t have an inductor (coil) in the circuit, you can set this to zero. Sowe have Z R 2 2 C. C is called the reactive capacitance and is measured in Ohms.Now examine the resistor equation as V R(t) V resistorsin( Dt). The maximum and minimumamplitudevoltage would oscillate across the resistor is V resistor Ramplitude Z V source.amplitudeImagine a sinusoidally driven RC circuit. If the capacitance is increased, explain what happens to theamplitude of the resistor voltage? Your explanation:If the frequency is increased what happens to the amplitude of the resistor voltage? Your answer:
Explain what happens to the current through the circuit if the resistor voltage amplitude decreases?Your explanation:Explain what happens to the power lost through heating the resistor if the resistor voltage amplitudedecreases? (Remember that P R =I R V R .) Your explanation:Imagine a sinusoidally driven RC circuit with source voltage amplitude V S , resistance R, and capacitanceC. Explain whether the resistor will become hotter if you increase the driving frequency? Use theconcept that Z = total impedance of the circuit. Your answer and explanation:1.4. The Capacitor Voltage Equation:V C(t) C V Z sourcesin Dt amplitude 2 The capacitor voltage oscillates sinusoidally and lags behind the resistor voltage by 90 o . Thereactive capacitance C is like the resistance of the capacitor and is measured in SI units of Ohms.The “resistance” of the capacitor is related to the capacitance of the capacitor and the drivingfrequency. This relationship C 1 can be derived from the differential equation modeling the DCcircuit, but you must memorize it. The larger the capacitance, the less “resistance” in the capacitor. Butjust as importantly if the driving frequency is increased, the “resistance” of the capacitor decreases. Thisis why a capacitor is often used as a high pass filter in electronics: the capacitor has less resistance tomore quickly oscillating currents. BE SURE TO REMEMBER THIS DURING TODAY’S LAB!If we rewrite the capacitor equation as V C(t) V capacitorsin Dt , the capacitor voltageamplitude 2 amplitude is given by V capacitor Camplitude Z V source. That means that the ratio of the capacitive reactance and theamplitudetotal circuit impedance times the source amplitude gives the amplitude of the voltage across the capacitor.In a previous equation, you found that the resistor voltage amplitude increases when the frequencyis increased. Since the voltage across the resistor and capacitor must add to the voltage across the source,if the resistor voltage amplitude increases, then the capacitor voltage must decrease. Therefore, as youincrease the driving frequency, the resistor voltage amplitude increases while the capacitor voltageamplitude decreases. (Not a question)
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Physics 241 Lab: RC Circuits â AC Source