JEE Main · 2024 · 31 Jan 2024 · Shift 1 · Capacitance

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A parallel plate capacitor with plate separation 5 mm is charged up by a battery. It is found that on introducing a dielectric sheet of thickness 2 mm, while keeping the battery connections intact, the capacitor draws 25% more charge from the battery than before. The dielectric constant of the sheet is ______.

Answer: 2

Solution

With the battery kept connected,

Q = C V

.

Without dielectric:

C_{0} = \frac{ε _{0} A}{d}

. With a dielectric slab of thickness

t = 2 mm

and constant

K

inserted in the gap

d = 5 mm

C = \frac{ε _{0} A}{d - t + t / K}

Since

Q \propto C

at fixed

V

, and

Q

increases by 25%:

\frac{C}{C _{0}} = 1.25 ⟹ \frac{d}{d - t + t / K} = 1.25

5 = 1.25 (3 + \frac{2}{K}) ⟹ 4 = 3 + \frac{2}{K} ⟹ K = 2

JEE Main · 2024 · 31 Jan 2024 · Shift 1 · Integer answer

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