Question

The Lissajous patterns are used to measure:

• A. Voltage and Current
• B. Power and Energy
• C. Frequency and Phase shift
• D. Resistance and Inductance

Hint:

A circular Lissajous pattern indicates that both signals have equal frequency and amplitude, with a phase shift of \( 90^\circ \) or \( 270^\circ \).
A straight line indicates a phase shift of \( 0^\circ \) or \( 180^\circ \).

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks for the electrical parameters that can be measured using Lissajous patterns on a Cathode Ray Oscilloscope (CRO).
Lissajous patterns are distinctive geometric figures displayed on an oscilloscope screen when two sinusoidal signals are applied simultaneously to the horizontal and vertical deflection plates.

Step 2: Key Formula or Approach:
The resulting shape of the Lissajous pattern depends on the ratio of the frequencies and the phase difference between the two applied signals.
- Phase Measurement: For two signals of equal frequency, the phase shift (\( \phi \)) is calculated using the intersection values on the Y-axis:
\[ \sin\phi = \frac{Y_1}{Y_2} \] Where \( Y_1 \) is the Y-intercept, and \( Y_2 \) is the maximum vertical deflection.
- Frequency Measurement: The frequency ratio is given by:
\[ \frac{f_y}{f_x} = \frac{\text{Number of horizontal tangencies}}{\text{Number of vertical tangencies}} \]

Step 3: Detailed Explanation:
Let us analyze how these measurements are conducted:

• Phase Difference Measurement:
- If the two signals are in phase (\( \phi = 0^\circ \)), the pattern is a straight line with a positive slope.
- If the phase difference is \( 90^\circ \), the pattern becomes a perfect circle (if amplitudes are equal) or an upright ellipse.
- If the phase difference is \( 180^\circ \), the pattern is a straight line with a negative slope.

• Frequency Ratio Measurement:
- By applying a signal of known frequency \( f_x \) to the horizontal axis and an unknown frequency \( f_y \) to the vertical axis, a stable pattern is displayed when the ratio \( f_y / f_x \) is a rational number.
- By counting the number of times the pattern touches horizontal and vertical reference lines, the unknown frequency can be calculated.

Step 4: Final Answer:
Lissajous patterns are used to measure frequency and phase shift.