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In a Schering bridge, the dial of the variable capacitor is calibrated directly in terms of the dissipation factor of the unknown arm. At 50 Hz frequency, the value of the dissipation factor of the unknown capacitor was found to be D. What would be the value of the dissipation factor at 60 Hz
- a)6 D
- b)1 / 6 D
- c)5 / 6 D
- d)6 / 5 D
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
In a Schering bridge, the dial of the variable capacitor is calibrated...
Concept:
Schering bridge:
At bridge balance condition,
At bridge balance condition,
⇒ R4Cx (1 + jωR3C3) = R3C1 (1 + jω Cx Rx)
By comparing both sides
Dissipation factor = ωCxRx = ωR3C3 = 2πf R3C3
Dissipation factor = ωCxRx = ωR3C3 = 2πf R3C3
Dissipation factor α frequency(f) --------(1)
Calculation:
Given:
Dissipation factor D at frequency 50Hz
Let Dissipation factor x at frequency 60Hz
From equation 1:
f1/f2 = D/z
x = 6/5 D
f1/f2 = D/z
x = 6/5 D
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In a Schering bridge, the dial of the variable capacitor is calibrated...
Dissipation Factor in Schering Bridge
The dissipation factor (D) of a capacitor is a measure of its efficiency, representing the ratio of the resistive power loss to the reactive power stored. The Schering bridge is commonly used to measure the dissipation factor at various frequencies.
Frequency Dependence of Dissipation Factor
- The dissipation factor varies with frequency.
- A higher frequency typically results in a lower dissipation factor due to reduced resistive losses in the capacitor.
Given Conditions
- At 50 Hz, the dissipation factor of the unknown capacitor is D.
- We need to determine the dissipation factor at 60 Hz.
Calculating the New Dissipation Factor
- The relationship between the dissipation factor and frequency can be approximated as:
\[ D_{60} = D_{50} \times \left( \frac{f_{50}}{f_{60}} \right) \]
- Substituting the known frequencies:
\[ D_{60} = D \times \left( \frac{50}{60} \right) \]
Final Calculation
- Rearranging gives:
\[ D_{60} = D \times \frac{5}{6} \]
Conclusion
- The dissipation factor at 60 Hz is \( \frac{5}{6} D \).
- Therefore, the correct answer is option **D: \(\frac{6}{5} D\)**.
This indicates that as frequency increases from 50 Hz to 60 Hz, the dissipation factor decreases, confirming the inverse relationship with frequency changes in capacitive elements.
The dissipation factor (D) of a capacitor is a measure of its efficiency, representing the ratio of the resistive power loss to the reactive power stored. The Schering bridge is commonly used to measure the dissipation factor at various frequencies.
Frequency Dependence of Dissipation Factor
- The dissipation factor varies with frequency.
- A higher frequency typically results in a lower dissipation factor due to reduced resistive losses in the capacitor.
Given Conditions
- At 50 Hz, the dissipation factor of the unknown capacitor is D.
- We need to determine the dissipation factor at 60 Hz.
Calculating the New Dissipation Factor
- The relationship between the dissipation factor and frequency can be approximated as:
\[ D_{60} = D_{50} \times \left( \frac{f_{50}}{f_{60}} \right) \]
- Substituting the known frequencies:
\[ D_{60} = D \times \left( \frac{50}{60} \right) \]
Final Calculation
- Rearranging gives:
\[ D_{60} = D \times \frac{5}{6} \]
Conclusion
- The dissipation factor at 60 Hz is \( \frac{5}{6} D \).
- Therefore, the correct answer is option **D: \(\frac{6}{5} D\)**.
This indicates that as frequency increases from 50 Hz to 60 Hz, the dissipation factor decreases, confirming the inverse relationship with frequency changes in capacitive elements.
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In a Schering bridge, the dial of the variable capacitor is calibrated directly in terms of the dissipation factor of the unknown arm. At 50 Hz frequency, the value of the dissipation factor of the unknown capacitor was found to be D. What would be the value of the dissipation factor at 60 Hza)6 Db)1 / 6 Dc)5 / 6 Dd)6 / 5 DCorrect answer is option 'D'. Can you explain this answer?
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