The spot in CRO is shifted upward by 4 cm when 10 volt dc is applied to its vertical input. Find maximum displacement of spot when 7 volt ac is applied to vertical input.

Steps to Solve

1. Identify given information The spot on the CRO is shifted 4 cm when a 10 V DC is applied. We need to find the maximum displacement when a 7 V AC is applied.

2. Calculate deflection sensitivity Using the formula: $$ \text{Deflection Sensitivity} = \frac{\text{Spot Shift}}{\text{Applied Voltage}} $$

For the given values:

• Spot Shift = 4 cm = 40 mm (since 1 cm = 10 mm)
• Applied Voltage = 10 V

Thus, $$ \text{Deflection Sensitivity} = \frac{40 \text{ mm}}{10 \text{ V}} = 4 \text{ mm/V} $$

3. Calculate peak voltage of 7 V AC For AC voltages, we use the peak value. The formula for converting RMS to peak value is: $$ V_{peak} = V_{rms} \times \sqrt{2} $$ For a 7 V RMS AC, we calculate: $$ V_{peak} = 7 \text{ V} \times 1.414 \approx 9.898 \text{ V} $$

4. Calculate maximum displacement for AC Using the deflection sensitivity calculated previously: $$ \text{Max Displacement} = \text{Deflection Sensitivity} \times V_{peak} $$ Substituting the values: $$ \text{Max Displacement} = 4 \text{ mm/V} \times 9.898 \text{ V} \approx 39.592 \text{ mm} $$

5. Convert to centimeters To express the final answer in centimeters: $$ \text{Max Displacement in cm} = \frac{39.592 \text{ mm}}{10} \approx 3.9592 \text{ cm} $$