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A parallel plate condenser with oil between the plates (dielectric constant of oil K = 2) has a capacitance C. If the oil is removed, then capacitance of the capacitors becomes
  • a)
    C/2
  • b)
    C/√2
  • c)
    2 C
  • d)
    √2C
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A parallel plate condenser with oil between the plates (dielectric con...
On removing the oil, the capacitance of the capacitor will become.
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A parallel plate condenser with oil between the plates (dielectric con...
Understanding Capacitance with Dielectrics
When considering a parallel plate capacitor, the presence of a dielectric material between the plates affects its capacitance. Here’s how it works:
Capacitance Formula
The capacitance (C) of a parallel plate capacitor is given by the formula:
C = (K * ε₀ * A) / d
Where:
- K is the dielectric constant (for oil, K = 2)
- ε₀ is the permittivity of free space
- A is the area of the plates
- d is the separation between the plates
Effect of Removing the Dielectric
1. Initial Condition with Oil:
- With oil between the plates, the capacitance is C = (2 * ε₀ * A) / d.
2. Condition after Removing Oil:
- When the oil is removed, the dielectric constant becomes 1 (for air or vacuum):
- The new capacitance (C') becomes C' = (1 * ε₀ * A) / d = (ε₀ * A) / d.
Calculating the New Capacitance
- Since the original capacitance C = (2 * ε₀ * A) / d, we can express C' in terms of C:
C' = C / 2
Conclusion
This shows that removing the oil reduces the capacitance to half its original value. Thus, the correct answer is:
Option A: C/2.
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