Which of the following expression is the correct formulae for the deflection sensitivity ‘S’ of a CRT, if D = deflection on the fluorescent screen L = distance from the center of the deflection plates to the screen Ld = effective length of the deflection plates d = distances between the deflection plates Ed = Potential between deflecting plates
Understanding CRT Deflection Sensitivity
The question asks for the correct formula for the deflection sensitivity of a Cathode Ray Tube (CRT). Deflection sensitivity (S) in a CRT is defined as the amount of deflection produced on the screen per unit deflecting voltage. It is a measure of how effectively the deflecting plates bend the electron beam.
Deriving the Deflection Sensitivity Formula
Let's first understand how the deflection D is produced on the screen. An electron beam enters the region between the deflection plates with a velocity determined by the accelerating voltage \(E_a\). When a potential difference \(E_d\) is applied across the deflection plates, an electric field is created between them. This field exerts a force on the electrons, causing them to accelerate perpendicular to their initial direction of motion while they are between the plates.
The deflection (vertical or horizontal) of the electron beam while it is between the deflection plates depends on the electric field (\(E_d/d\)), the length of the plates (\(l_d\)), and the electron's initial velocity. After leaving the deflection plates, the electron travels in a straight line to the screen. The total deflection D on the screen is proportional to the angle of deflection upon leaving the plates and the distance from the plates to the screen (L).
The formula for the total deflection D on the screen is given by:
\(D = \frac{E_d L l_d}{2 d E_a}\)
Where:
- \(D\) is the deflection on the fluorescent screen.
- \(L\) is the distance from the center of the deflection plates to the screen.
- \(l_d\) is the effective length of the deflection plates.
- \(d\) is the distance between the deflection plates.
- \(E_d\) is the potential difference between the deflecting plates.
- \(E_a\) is the accelerating voltage.
Deflection sensitivity \(S\) is defined as the deflection D per unit deflecting voltage \(E_d\):
\(S = \frac{D}{E_d}\)
Now, substitute the expression for D into the definition of S:
\(S = \frac{\frac{E_d L l_d}{2 d E_a}}{E_d}\)
Simplify the expression by canceling \(E_d\) from the numerator and denominator:
\(S = \frac{L l_d}{2 d E_a}\)
This is the formula for the deflection sensitivity S of a CRT.
Analyzing the Options
Let's compare our derived formula with the given options:
- Option 1: \(S = \frac{{L{l_d}}}{{2{d^2}{E_a}}}\). This option has \(d^2\) in the denominator, which is incorrect.
- Option 2: \(S = \frac{{2d{E_a}}}{{L{l_d}n}}\). This option has the terms inverted and an extra factor 'n', which is incorrect.
- Option 3: \(S = \frac{{L{l_d}}}{{2d{E_d}}}\). This option has the deflecting voltage \(E_d\) in the denominator instead of the accelerating voltage \(E_a\). This is incorrect. \(E_a\) is in the denominator because a higher accelerating voltage means faster electrons, which spend less time between the deflecting plates, resulting in less deflection for the same deflecting voltage.
- Option 4: \(S = \frac{{L{l_d}}}{{2d{E_a}}}\). This option exactly matches our derived formula.
Therefore, the correct formula for the deflection sensitivity S of a CRT is \(S = \frac{{L{l_d}}}{{2d{E_a}}}\).
Conclusion
Based on the derivation and comparison with the options, the correct formula for the deflection sensitivity S of a CRT is \(S = \frac{{L{l_d}}}{{2d{E_a}}}\).
Revision Table: CRT Deflection Formula Parameters
| Symbol | Parameter | Description | Units (typically) |
|---|---|---|---|
| \(S\) | Deflection Sensitivity | Deflection per unit deflecting voltage | m/V or cm/V |
| \(D\) | Deflection on screen | Distance the spot moves on the screen | m or cm |
| \(L\) | Screen Distance | Distance from center of deflection plates to screen | m or cm |
| \(l_d\) | Plate Length | Effective length of deflection plates | m or cm |
| \(d\) | Plate Separation | Distance between deflection plates | m or cm |
| \(E_d\) | Deflecting Voltage | Potential difference across deflection plates | Volts (V) |
| \(E_a\) | Accelerating Voltage | Voltage accelerating the electron beam | Volts (V) |
Additional Information: CRT Deflection Factor
Related to deflection sensitivity is the deflection factor, often denoted by G. The deflection factor is the reciprocal of the deflection sensitivity.
Deflection Factor \(G = \frac{1}{S}\)
It represents the deflecting voltage required to produce a unit deflection on the screen.
Using the formula for S, the formula for the deflection factor G is:
\(G = \frac{1}{\frac{L l_d}{2 d E_a}} = \frac{2 d E_a}{L l_d}\)
The units for deflection factor are typically Volts/meter (V/m) or Volts/centimeter (V/cm).
Understanding both deflection sensitivity and deflection factor is crucial for analyzing the performance of a CRT in applications like oscilloscopes.
Important Questions from Cathode Ray Oscilloscope
The function of a trigger level knob on a CRO is:
Aquadag coating is most commonly used in CROs to:
CRO stands for:
Calculate the maximum velocity of the beam of electrons in a CRT having a cathode and anode voltage of 182 V. Assume that the electrons leave the cathode with zero velocity. (Charge of electron = 1.6 × 10-19 C and mass of electron = 9.1 × 10-31 kg)
Trigger pulses in CRO are used -
