The spot in CRO is shifted upward by 4 cm when 10 volt dc is applied to its vertical input. Find maximum displacement of the spot when 7 volt ac is applied to vertical input.
Understand the Problem
The question describes a problem involving a spot on a cathode ray oscilloscope (CRO) that shifts due to the application of a DC voltage and then requests the calculation of maximum displacement when an AC voltage is applied. It involves understanding the principles of deflection sensitivity and voltage effects on a CRO.
Answer
The maximum displacement when 7V AC is applied is $2.8 \, \text{cm}$.
Answer for screen readers
The maximum displacement when 7V AC is applied is $2.8 , \text{cm}$.
Steps to Solve
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Calculate Deflection Sensitivity The problem states that a DC voltage of 10V causes a vertical deflection of 4 cm on the CRO. We can find the deflection sensitivity (DS) using the formula: $$ DS = \frac{\text{Spot shift}}{\text{Applied voltage}} $$ Substituting the values: $$ DS = \frac{4 , \text{cm}}{10 , \text{V}} = 0.4 , \text{cm/V} $$
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Calculate Maximum Displacement for AC Voltage Now, we need to find the maximum displacement when 7V AC is applied. We use the same deflection sensitivity: $$ \text{Max Displacement} = DS \times \text{Applied AC voltage} $$ Substituting the previously calculated DS and the AC voltage: $$ \text{Max Displacement} = 0.4 , \text{cm/V} \times 7 , \text{V} = 2.8 , \text{cm} $$
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Final Result Therefore, the maximum displacement on the CRO when 7V AC is applied is: $$ 2.8 , \text{cm} $$
The maximum displacement when 7V AC is applied is $2.8 , \text{cm}$.
More Information
In cathode ray oscilloscopes, deflection sensitivity is essential for translating voltage into visual displacement. This problem illustrates how both DC and AC voltages influence the position of the spot on the screen.
Tips
- Failing to convert units properly. Ensure all measurements are in consistent units (e.g., centimeters and volts).
- Misapplying the deflection sensitivity formula. Remember that sensitivity is calculated using the ratio of deflection to applied voltage.
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