AC Circuits ITJ

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AC Circuits I & II

Terry Jones

Austin Harris

Physics 231

07/27/11-08/01/11



Objectives: The objectives of this experiment are: 1) to study the time dependence of current

and voltage in resistors, capacitors, and inductors in a simple circuit with an alternating current

(AC) source, 2) to measure the maximum current and voltage values in some simple AC circuits

and their dependence on the AC frequency, 3) to study and measure the phase relationships

between the AC current source and the voltages across resistor, capacitor, and inductor elements,

and 4) to study and measure the resonant frequency in a simple resistor-inductor-capacitor (RLC)

circuit.

Apparatus: The apparatus consists of: 1) a Pasco CI-6512 RLC circuit board containing a

selection of resistors and capacitors and a variable inductor, 2) a Pasco Science Workshop 750

Interface computer data acquisition and control system, 3) computer system with Pasco

DataStudio software, and 4) voltage probe and leads with banana plugs.

Theory: This experiment is concerned with some simple alternating current (AC) circuits

containing resistor, capacitors, and inductors and the effect these devices have on the flow of

current. The emf source for these circuits varies sinusoidally. This sinusoidally varying voltage

can be described by the equation V’s=V’sm cos (omega * time) where V’s is the instantaneous

voltage of the AC source at any instant of time t. Similarly, the current supplied by an AC

source can be described I’s = I’sm cos (omega*time) where I’s is the instantaneous current at

time t and I’sm is the amplitude of the current.

AC Circuit with Resistor

In a simple AC circuit consisting of an AC source and a resistance R, the voltage across the

resistance, V’r will be given by Ohm’s law to be V’r=I’s*R since the current is the same in all

parts of the circuit.

AC Circuit with Capacitor



In a simple AC circuit consisting of an AC source and a capacitor C, the voltage across the

capacitor, V’c will vary periodically with time with the same frequency as the AC source, but out

of phase with a phase angle difference of phi and V’c=V’cm cos(omega*t + phi). Substituting

phi = -pi/2 into the above equation for the voltage and comparing it to earlier equations for the

output current, gives the relationships V’c = V’cm cos(omega*t-(pi/2)) and I’s=I’sm

cos(omega*t) that show that the output current, I’s, leads the voltage across the capacitor, V’c,

by a phase angle of –pi/2.

AC Circuit with Inductor

In a simple AC circuit consisting of an AC source and a inductor L, the voltage across the

inductor, V’L, will vary periodically with time with the same frequency as the AC source, but

out of phase with the source current with a phase angle difference of phi. As in case of

capacitance reactance, the inductive reactance, X’L, is measured in units of ohms and can be

determined by measureing the amplitudes of the inductor voltage and the source output current

with X’L= omega*L. omega= 1/sqrt(LC).



Data Results:



Error Analysis: In the experiment there is a measure of error that is difficult to avoid given the

circumstances and nature of obtaining measurements with faulty equipment. There is also a

measure of error with any experiment involving measurements of resistors and capacitors and

inductors because of their inherent tendencies to over-heat and fully charge and discharge,

respectively.

Conclusion: Capacitors affect the flow of current when changes in potential occur by.

Inductors affect the flow of current when changes in potential occur by. Resistors also affect the

flow of current. It was determined that the value for the time constant was measured correctly by

graphical analysis. By using our measurements obtained by the equipment we were able to

successfully graph our results with comparable accuracy and precision. Our calculations for the

time constant voltages are supported by the data as well. The data collected can also be proven

true by the equation relationships determined in the theory above.

AC Circuits ITJ

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