Lab Report 2: Measurement of AC Quantities using Oscilloscope

1. OBJECTIVES

• To be able to use an oscilloscope and function generator.
• To study and be able to measure the AC wave by using a graph and cursor.

2. INSTRUMENTS REQUIRED

• Oscilloscope
• Function generator
• AC source

3. THEORY

AC Current

AC current is an electric current that periodically changes direction, flowing first in one direction and then in the opposite direction. The mathematical representation of AC is typically expressed as a sinusoidal function.

i.e., \(I(t) = I_{peak} \cdot \sin(\omega t + \phi)\)

Inductor (L)

An inductor is a passive electrical component that stores energy in a magnetic field when current flows through it. Inductive reactance (\(X_L = 2\pi fL\)).

Capacitor (C)

A capacitor is a passive electrical component that stores energy in an electric field between its plates when voltage is applied.

RL Circuit

An RL circuit consists of a resistor and an inductor connected in series.

RC Circuit

An RC circuit consists of a resistor and a capacitor connected in series.

Oscilloscope

An oscilloscope is a versatile electronic instrument primarily used to display and analyze the waveform of electrical signals.

Function Generator

A function generator is an electronic test instrument used to generate different types of electrical waveforms over a wide range of frequencies.

RMS Value

The RMS (Root Mean Square) value of an AC is the value of DC that, when flowing through a circuit or resistor for a specific time period, produces the same amount of heat as is produced by the alternating current when flowing through the same circuit or resistor for the same amount of time.

\(V_{RMS} = \frac{V_{p-p}}{2\sqrt{2}}\)

Average Value

If we convert the AC sine wave into a DC sine wave through rectifiers, then the converted DC value is known as the average value of that alternating current sine wave.

\(V_{avg} = \frac{V_{p-p}}{\pi}\)

4. CIRCUIT DIAGRAMS FOR EXPERIMENT

For R-L Series Circuit:

\(\phi = \tan^{-1}\left(\frac{X_L}{R}\right)\)

\(V_R = I \times R\)

\(V_L = I \times X_L\)

For R-C Series Circuit:

\(\phi = \tan^{-1}\left(\frac{X_C}{R}\right)\)

\(V_R = I \times R\)

\(V_C = I \times X_C\)

5. OBSERVATION

i. For 50Hz sinewave:

• Vertical deflection = 5 cm
• Volt/cm = 1 V/cm
• \(V_{p-p}\) = (Vertical deflection/cm) x (V/cm) = 5 V
• \(V_{rms} = \frac{V_{p-p}}{2\sqrt{2}} = \frac{5}{2\sqrt{2}} = 1.767 V\)
• \(V_{avg} = \frac{V_{p-p}}{\pi} = \frac{5}{\pi} = 1.59 V\)
• Horizontal deflection = 4 cm
• Time/cm = 5 ms/cm = \(5 \times 10^{-3}\) s/cm
• Time period (T) = 0.02 sec
• Frequency (\(f = \frac{1}{T}\)) = \(\frac{1}{0.02} = 50 Hz\)

ii. For 500Hz sinewave:

• Vertical deflection = 5 cm
• Volt/cm = 2 V/cm
• \(V_{p-p}\) = (Vertical deflection/cm) x (V/cm) = 5 x 2 = 10 V
• \(V_{rms} = \frac{V_{p-p}}{2\sqrt{2}} = \frac{10}{2\sqrt{2}} = 3.535 V\)
• \(V_{avg} = \frac{V_{p-p}}{\pi} = \frac{10}{\pi} = 3.18 V\)
• Horizontal deflection = 4 cm
• Time/cm = 500 µs/cm = 0.0005 s/cm
• Time period (T) = 0.002 sec
• Frequency (\(f = \frac{1}{T}\)) = \(\frac{1}{0.002} = 500 Hz\)

6. CALCULATION

1. Error calculation for 50Hz sinewave:

% Error = \(|\frac{f_{actual} – f_{calculated}}{f_{actual}}| \times 100\%\)

= \(|\frac{50 – 50}{50}| \times 100\% = 0\%\)

2. Error calculation for 500Hz sine wave:

% Error = \(|\frac{f_{actual} – f_{calculated}}{f_{actual}}| \times 100\%\)

= \(|\frac{500 – 500}{500}| \times 100\% = 0\%\)

7. RESULT

• Frequency calculated for 50Hz sinewave = 50Hz
• Frequency calculated for 500Hz sinewave = 500Hz

8. DISCUSSIONS

The experiment was performed with the help of a dual-channel cathode ray oscilloscope. It was used to measure amplitude, frequency, voltage, and time period. The circuit was adjusted and the oscilloscope was set in such a way as to get a fine line display. From the obtained horizontal deflection of the wave, the time period and frequency were calculated. From the vertical deflection, V(peak-to-peak), Vrms, and Vavg were calculated respectively. In this experiment, there was no error obtained.

9. CONCLUSION

Hence, AC quantities were measured with the help of an oscilloscope. The phase relation of RL and RC loads was also studied.

10. PRECAUTIONS

• The intensity and focus of the oscilloscope should be adjusted in such a way as to get a fine line display.
• The signal generator should be set to a particular magnitude and frequency.
• The zero adjustment should be managed with care.