The deflection sensitivity of a CRT is 0.03 mm/V. An unknown voltage applied to X-plates causes the deflection of spot 3 mm horizontally. Find the value of unknown voltage.
Understand the Problem
The question is asking to calculate the unknown voltage applied to the X-plates of a CRT based on the given deflection sensitivity and the amount of deflection observed.
Answer
The unknown voltage applied to the X-plates is $100 \text{ V}$.
Answer for screen readers
The value of the unknown voltage applied to the X-plates is $100 \text{ V}$.
Steps to Solve
- Identify the formula for applied voltage
To find the applied voltage, we use the formula derived from the relationship between deflection sensitivity, applied voltage, and deflection (spot shift).
- Write down the known values
- Deflection sensitivity: $0.03 \text{ mm/V}$
- Spot shift (deflection): $3 \text{ mm}$
- Set up the calculation
Using the relationship:
$$ \text{Applied Voltage} = \frac{\text{Spot Shift}}{\text{Deflection Sensitivity}} $$
Substituting the known values into the equation:
$$ \text{Applied Voltage} = \frac{3 \text{ mm}}{0.03 \text{ mm/V}} $$
- Calculate the applied voltage
Now, perform the calculation:
$$ \text{Applied Voltage} = \frac{3}{0.03} = 100 \text{ V} $$
The value of the unknown voltage applied to the X-plates is $100 \text{ V}$.
More Information
In this problem, the concept of deflection sensitivity in CRTs is important, as it relates the amount of voltage applied to the extent of horizontal deflection on the screen. The calculated voltage indicates how much electrical potential is needed to achieve that specific level of deflection.
Tips
- Misunderstanding the units: Ensure that the deflection sensitivity is in the correct units (mm/V) and the spot shift is also in mm before performing the calculations.
- Failing to convert units: Always check if the values given need to be converted into compatible units (though in this case, both are in mm).
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