The deflection sensitivity (s) of a CRT (cathode ray tube) is defined as: (where D is deflection of the screen

Question

The deflection sensitivity (s) of a CRT (cathode ray tube) is defined as: (where D is deflection of the screen and E is defection voltage)

Examoogle · Accepted Answer

The correct answer is Option D: $s = \frac{D}{E}$. Deflection sensitivity is defined as the amount of deflection produced on the screen per unit of deflection voltage applied. Mathematically, it is the ratio of the beam deflection $D$ to the voltage $E$ applied across the deflection plates, expressed as $s = \frac{D}{E}$.

Step-by-Step Solution & Concepts:
Deflection sensitivity is defined as the amount of deflection produced on the screen per unit of deflection voltage applied. Mathematically, it is the ratio of the beam deflection $D$ to the voltage $E$ applied across the deflection plates, expressed as $s = \frac{D}{E}$.

Working Principle: In a cathode ray tube (CRT), electrons are accelerated and pass through a pair of deflection plates. When a potential difference $E$ is applied across these plates, an electric field is created, exerting a force on the electrons that causes a lateral displacement $D$ on the fluorescent screen. The sensitivity represents how responsive the beam is to the input voltage.

Key Formulas: $s = \frac{D}{E}$ — sensitivity formula where $s$ is sensitivity, $D$ is deflection distance, and $E$ is deflection voltage.; $D = \frac{L d E}{2 d_a V_a}$ — common expression for beam deflection, where $L$ is screen distance, $d$ is plate length, $d_a$ is plate separation, and $V_a$ is accelerating voltage.

Key Points: Deflection sensitivity is measured in units of meters per volt ($m/V$) or centimeters per volt ($cm/V$).; It is inversely proportional to the accelerating voltage ($V_a$) of the electron beam.; Higher sensitivity means the beam is easier to deflect with a smaller voltage.

Advantages: Allows for measurement of low-voltage signals in oscilloscopes.

Disadvantages: High sensitivity can sometimes lead to non-linear beam behavior or distortion if not properly calibrated.

Applications: Cathode Ray Oscilloscopes (CRO); Analog television displays

Additional Info: The inverse of deflection sensitivity is known as the 'deflection factor' or 'deflection coefficient', defined as $G = \frac{E}{D} = \frac{1}{s}$.. Option A ($s = (D/E)^2$), Option B ($s = D 	imes E$), and Option C ($s = \sqrt{D/E}$) are incorrect dimensions and do not represent the linear relationship between deflection and voltage.

Answer: D is correct — deflection sensitivity is defined as the ratio of screen deflection to the deflection voltage.

Exam Tip: Always check the units; since sensitivity is (meters/volts), the formula must represent 'displacement divided by voltage'. Don't confuse sensitivity with the deflection factor, which is the reciprocal.

Examoogle · Answer

Option A: $s = \left(\frac{D}{E}\right)^2$

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Option B: $s = D 	imes E$

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Option C: $s = \sqrt{\frac{D}{E}}$

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