Match the following Lissajous figures to their vertical deflection voltage graph.

This question was previously asked in

UPPCL JE EC Official Paper (Held on 25 March 2021: Shift 1)

Option 4 : 1 - c, 2 - a, 3 - d, 4 - b

CT 1: Network Theory 1

11608

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**Concept-**When both pairs of the deflection plates (horizontal deflection plates and vertical deflection plates) of CRO (Cathode Ray Oscilloscope) are connected to two sinusoidal voltages, the patterns appear at CRO screen are called the Lissajous pattern. Shape of these Lissajous pattern changes with changes of phase difference between signal and ration of frequencies applied to the deflection plates (traces) of CRO.

**Case – 1: When ø=0 or ø=360**

when the angle is ø = 0 or ø = 360, the Lissajous pattern is of the shape of straight line passing through origin from first quadrant to third quadrant.

**Case – 2: When, 0 < ø < 90 or 270 < ø <360 : –**

when the angle is in the range of 0 < ø < 90 or 270 < ø < 360, the Lissajous pattern is of the shape of Ellipse having major axis passing through origin from first quadrant to third quadrant.

**Case – 3: When ø=90**

when the angle is ø = 90 the Lissajous pattern is of the shape of circle.

**Case – 4: When 90 < ø < 180 or 180 < ø < 270**

when the angle is in the range of 0 < ø < 90 or 270 < ø < 360, the Lissajous Pattern is of the shape of Ellipse having major axis passing through origin from second quadrant to fourth quadrant.

**Case – 5: When ø=180**

when the angle is ø = 180 the Lissajous pattern is of the shape of straight line passing through origin from second quadrant to fourth quadrant.

** Solution**:-

Let at horizontal plate voltage graph is

**Option-1**:- It is of case (1) so at vertical plate voltage graph will be with phase difference ϕ = 0 or 360°

**Option-2**:- It is of case (2) so 0 < ϕ < 90° so at vertical plate voltage graph will have phase difference of 0 < ϕ < 90°

**Option-3**:- It is of case (3) so ϕ = 90° ↑ vertical voltage graph of have ϕ = 90° w.r.t horizontal voltage graph

**Option-4**:- It is of case (4) so 90° < ϕ < 180°, vertical voltage graph will have phase difference 90° < ϕ < 180° w.r.t. horizontal voltage graph