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Capacitance of a capacitor becomes 7 6 times its original value if a dielectric slab of thickness, t = 2/3 d is introduced in between the plates. 'd' is the separation between the plates. The dielectric constant of the dielectric slab is
  • a)
    14 /11
  • b)
    11/14
  • c)
    7/11
  • d)
    11/7
Correct answer is option 'A'. Can you explain this answer?
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Given:
- Capacitance of a capacitor becomes 7 times its original value when a dielectric slab is introduced between the plates.
- Thickness of the dielectric slab, t = 2/3d, where d is the separation between the plates.

To find:
The dielectric constant of the dielectric slab.

Solution:
The capacitance of a parallel plate capacitor is given by the formula:

C = (K * ε₀ * A) / d

Where,
C = Capacitance
K = Dielectric constant
ε₀ = Permittivity of free space
A = Area of the plates
d = Separation between the plates

Step 1: Original Capacitance
Let's assume the original capacitance of the capacitor is C₀.

C₀ = (K₀ * ε₀ * A) / d

Step 2: Capacitance with Dielectric Slab
When a dielectric slab is introduced between the plates, the capacitance becomes 7 times its original value.

C = 7C₀

Substituting the original capacitance equation into the above equation:

(K * ε₀ * A) / d = 7 * (K₀ * ε₀ * A) / d

Step 3: Thickness of Dielectric Slab
Given that the thickness of the dielectric slab, t = 2/3d.

t = 2/3d

Multiplying both sides by d:

td = 2/3d^2

Canceling out 'd' from both sides:

t = 2/3d

Step 4: Ratio of Capacitances
We can express the ratio of the capacitances as:

C / C₀ = K / K₀

Substituting the values from Step 2:

7C₀ / C₀ = K / K₀

Simplifying the equation:

7 = K / K₀

Step 5: Finding the Dielectric Constant
To find the dielectric constant, we need to find the ratio K / K₀.

From Step 4, we have:

7 = K / K₀

Multiplying both sides by K₀:

7K₀ = K

Therefore, the dielectric constant of the dielectric slab is 7 times the original dielectric constant.

Given that the original dielectric constant is K₀ = 1, the dielectric constant of the dielectric slab is:

K = 7 * 1 = 7

Hence, the correct answer is option 'A' (7/1 or 7).
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Capacitance of a capacitor becomes 7 6 times its original value if a dielectric slab of thickness, t = 2/3 d is introduced in between the plates. 'd' is the separation between the plates. The dielectric constant of the dielectric slab isa)14 /11b)11/14c)7/11d)11/7Correct answer is option 'A'. Can you explain this answer?
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