course material

1. PHYS 2212L Principles Of Physics II Lab
Answer:
Introduction
This Experiment is the first of two in which AC circuits will be more explicitly introduced. As
a result of using an oscilloscope, we may determine the voltage response and impedance
response to the frequency of an AC signal that has passed through a series circuit consisting
of a resistor and capacitor (RC), and a resistor & inductor (RL).
Background And Theory
The amount and direction of the current fluctuate with time in AC circuits. The magnitude
and polarity of voltage decreases across elements change with time. During the late 19th
century, Nikola Tesla established that AC's time-varying current and voltage is the most
effective method of delivering electricity. This can be illustrated as shown in the figure
below; (Lab06Manual)
Figure 1: Graph of Amplitude Vs Time
The sine waveform, as depicted in the image above, is the most commonly encountered
time-varying AC signal. There is a distinct peak voltage in the graph, which rises to zero
before returning to zero. The voltage then reverses its polarity, starting at zero, falling to a
negative maximum value, and then returning to zero. Similarly, when the polarity of the
voltage changes from positive to negative, so does the current (switching directions,
forward then backward). Charges move in a wavelike pattern via the wires. This lab will
study a few of the effects that are only seen in AC circuits because of the fluctuating current
and voltage. (Lab06Manual) (Bhargava & Kulshreshtha)
Definition Of Terms
From the above graph shown in figure 1, the following terms may be defined as shown
below; (Lab06Manual).
Amplitude

2. This is the absolute maximum displacement of current or voltage on either side of the mean
position. For instance, from the above graph, the amplitude is 10 Volts.
Peak -To- Peak Voltage
This is the difference in voltage or current between the highest and lowest values. From the
above graph, this value is 20 Volts.
Period
This is the time taken by a waveform to form one complete oscillation. The horizontal
displacement in time units can be measured between any two corresponding positions,
from peak to peak, trough to trough, or any other two corresponding places.
Frequency
This is generally the number of complete cycles or oscillations forms in one second.
Mathematically, it is the reciprocal of the period.
AC voltage peak-to-peak measurements are easy with an oscilloscope . The voltage
difference between the signal's peak and trough is what we're interested in. If the signal's
amplitude is doubled, the peak-to-peak voltages will be twice as high. We can eliminate this
two-fold error if we measure all voltages from the highest to the lowest point.
Capacitors, Resistors, And Inductance Mode
It's possible to store electrical energy in the form of a charge using a capacitor. Separated by
a non-conducting substance are two or more conducting electrodes (the dielectric). A
capacitor doesn't conduct any current. When a voltage is supplied across the electrodes,
charges build up (or down) on the plates. The capacitance of a capacitor determines the
maximum charge it can carry at any given potential. (C). mathematically;
Capacitance is measured in Farads, which is equivalent to seconds per ohm, . (Bhargava &
Kulshreshtha) (Lab06Manual)
The charge accumulated at the electrodes of the capacitor determines the voltage across it
at any given moment t. There is a long buildup period before that charge may be felt (or
down). Voltage and current reverse direction too quickly when driven by an AC signal with
a high frequency, causing the capacitor to begin discharging before it has a chance to fully
charge. Therefore, the voltage across a capacitor is inversely proportional to the frequency
of the AC signal and reduces at higher frequencies, and increases at lower frequencies.

3. As a result, the voltage across the capacitor and the current flowing through the circuit have
a lag period. To put it another way, when it comes to voltage, the current is out of sync with
the voltage. A quarter of a cycle separates the voltage of the capacitor (Lab06Manual)or
from the current. The current and voltage across the capacitor are out of phase by 90° if we
consider 360° as one full cycle.
The coil of wire that makes up an inductor might have or not have a core. To counteract the
EMF of the time-varying voltage applied to the coil, a back-EMF is generated when a time-
varying current is passed through it. Depending on the frequency of the AC signal, the back-
EMF can be large or small; at higher frequencies, the effect is more pronounced, whereas, at
lower frequencies, the effect is less pronounced. A direct current inductor is essentially a
piece of wire at zero frequency, therefore there is no effect. Inductance determines the
greatest amount of back-EMF that may be created by an inductor at any given changing
current (L). Mathematically;
The inductance is measured in Henry (H), which is equivalent to .
The voltage across the inductor and the current across the circuit are in phase with each
other, just like the capacitor is. When it comes to the inductor, however, the current lags
behind the voltage by . A resistor does not affect the phase relationship between voltage and
current because resistance does not affect frequency. In other words, current and voltage in
an AC circuit are always in phase. (Bhargava & Kulshreshtha) (Lab06Manual)
Phase shift is calculated by comparing the times of two corresponding peaks or valleys (any
two adjacent corresponding points suffice as well). It is possible to compute the phase shift
(in degrees) of an AC generator.
Impedance And Reactance
Like resistors, inductors and capacitors obstruct the flow of current in an AC circuit when
they are operating in this mode. Their impedance, however, differs from that of a resistor
fundamentally. Inductors and capacitors react to the flow of current, and their resistance to
current flow is called reactance, as described earlier. The unit of reaction is the ohm (?), and
the symbol for it is
where is the frequency of the AC signal and C is the capacitance of the capacitor, and is the
symbol for its reactance.
It's important to note that the reactance is larger at lower frequencies, while the reactance
decreases as the frequency increases. Taking the DC limit into account, the reactance is
infinite as the frequency approaches zero. Because the capacitance gap is infinitely resistive,
the capacitor is effectively a barrier to the flow of current. At its most extreme, the reaction
has no value because the frequency is approaching infinity. Due to the rapidity with which

4. the current oscillates at high frequencies, the gap is mostly irrelevant, and the resistance is
minimal.
Since both and are functions of time, they are analogous to Ohm's Law, which describes the
resistance of a DC circuit.
At low frequencies, the reactance is small, whereas, at high frequencies, the reactance is
large. This behavior is consistent. Once again, as the frequency approaches 0 (the DC limit),
the reactance is zero, which is exactly what one would expect. All an inductor is is a wire
through which no resistance is encountered by the current it carries. Reactance becomes
limitless when frequency approaches infinity. The inductor creates enough back-EMF to
halt the current while operating at high frequencies because the current oscillates so
rapidly. The drop in voltage across the inductor is given by the following equation:
(Lab06Manual)
The voltage drop across the resistor is given by the following equation:
There is no frequency response in resistors; they nevertheless obey Ohm's law.
Experimental Set Up
Parts A and B are involved in the experiment. It was determined that the peak-to-peak
voltages for two pairs of series AC circuits containing a resistor and capacitor parts were
tested. Between the resistor and capacitor, the phase shifts were detected and measured. In
addition, the frequency at which the voltage decreases across the elements is equal was
established. Peak-to-peak voltages and currents, as well as the AC impedance of the circuit,
were calculated using the resulting data.
A decade resistance box was used to create resistances. The equipment kit is as shown
below;
In Kit-return to kit
Red & Black Banana leads
Yellow & Blue Banana leads
Set 1 1x capacitor
Set 2 1x capacitor
2x Dongles
Decade Resistance Box
In Drawer-Return Drawer
Ruler

5. Protractor
Available in the Lab
Green LCR Meter
Signal Generator
Oscilloscopes
Set Up
Setup the AC Generator and the Oscilloscope
The AC Generator and the Oscilloscope were set using the steps and instructions of the
Machine manual found in the laboratory. This was then followed with machine setups to
acquire the average settings and the peak-to-peak voltage measurements settings. The
experiment was then carried out for PART A and PART B as illustrated below;
Part A
This was set as AC circuit set 1. It was done by using the components of set 1:
The test frequency was set to .
The decade resistance box was set as the resistor and the required adjustments s per the lab
manual were done appropriately.
The values of the were then measured using the .
The value of the test frequency was then measured using the AC generator.
The peak-to-peak voltage for the resistor and capacitor was then recorded.
The defined voltage in the A.C generator was then labeled as .
Other adjustments were then made and all the data recorded.
Part B
This was set as AC circuits set 2. The components of AC circuit components were as follows:
The frequency was then set to
All the procedures and adjustments used in PART A as per the lab manual were then
repeated using the components of the resistance values for set 2.
The A.C generator and the Oscilloscopes were then turned OFF and the circuit disassemble.
This is a positive shift since the calculated is leading with a positive deviation of .
Conclusion
The objective of the experiment to examine the concepts of the alternating circuits was
successfully achieved. Both the voltage response and the impedance response were
effectively examined to the frequency of an alternating signal that was sent to the

6. Resistor/capacitor series circuits and Resistor/inductor series circuits.
References
Bhargava, N., & Kulshreshtha, D. (n.d.). Basic Electronics & Linear Circuits. Tata McGraw-Hill
Education.
Lab06Manual. (n.d.). AC Circuits lab manual.