Q20. A slab of material of dielectric constant k has the same area as the plates of a parallel plate

Q: What is the correct answer for CUET UG Physics Q20?

The correct answer is B. The capacitance of a parallel plate capacitor with a vacuum (or air) between its plates is C₀ = ε₀A/d, where A is the area of the plates and d is the separation between them. When a dielectric slab of thickness 't' and dielectric constant 'k' is inserted between the plates, the capacitance becomes C = ε₀A / (d - t + t/k). Given: thickness of dielectric slab t = 3d/4. Substitute t into the formul

Q: Q20. A slab of material of dielectric constant k has the same area as the plates of a parallel plate capacitor, but has a thickness 3d/4. Where d is the distance between plates of capaciptor. The…

The correct answer is B. The capacitance of a parallel plate capacitor with a vacuum (or air) between its plates is C₀ = ε₀A/d, where A is the area of the plates and d is the separation between them. When a dielectric slab of thickness 't' and dielectric constant 'k' is inserted between the plates, the capacitance becomes C = ε₀A / (d - t + t/k). Given: thickness of dielectric slab t = 3d/4. Substitute t into the formul

Q: What are the options for this CUET UG Physics question?

A. 4k / (3k+4) · B. 4k / (k+3) · C. 5k / (k+2) · D. k / (k+3)

Question

Q20. A slab of material of dielectric constant k has the same area as the plates of a parallel plate capacitor, but has a thickness 3d/4. Where d is the distance between plates of capaciptor. The ratio of the capacitance with dielectric inside it to its capacitance without the dielectric is:
(a) 4k / (3k+4)
(b) 4k / (k+3)
(c) 5k / (k+2)
(d) k / (k+3)

FirstInTest · Accepted Answer

The capacitance of a parallel plate capacitor with a vacuum (or air) between its plates is C₀ = ε₀A/d, where A is the area of the plates and d is the separation between them. When a dielectric slab of thickness 't' and dielectric constant 'k' is inserted between the plates, the capacitance becomes C = ε₀A / (d - t + t/k). 
Given: thickness of dielectric slab t = 3d/4. 
Substitute t into the formula for C:
C = ε₀A / (d - (3d/4) + (3d/4)/k)
C = ε₀A / (d/4 + 3d/(4k))
C = ε₀A / (d * (1/4 + 3/(4k)))
C = ε₀A / (d * (k + 3)/(4k))
C = (4kε₀A) / (d(k + 3))
Now, we need to find the ratio of the capacitance with the dielectric (C) to the capacitance without the dielectric (C₀): 
C/C₀ = [(4kε₀A) / (d(k + 3))] / [ε₀A/d] 
C/C₀ = 4k / (k + 3). 
Therefore, option (b) is the correct ratio.

Answer

4k / (3k+4)

Answer

4k / (k+3)

Answer

5k / (k+2)

Answer

k / (k+3)

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