Capacitors

JEE Main level, numerical answer, medium

80 of 180

Question 80 of 180

A parallel plate capacitor with plate separation 5mm5mm is charged up by a battery. It is found that on introducing a dielectric sheet of thickness 2mm2mm, while keeping the battery connections intact, the capacitor draws 2525% more charge from the battery than before. The dielectric constant of the sheet is ____.

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Answer: 2

Without dielectric, capacitance will be C=Aϵ0dC=\dfrac{A{\epsilon }_{0}}{d}.
Therefore, charge on it, Q=Aϵ0dVQ=\dfrac{A{\epsilon }_{0}}{d}V
Now, with dielectric capacitance will be C′=Aϵ0d−t+tK{C}^{'}=\dfrac{A{\epsilon }_{0}}{d-t+\dfrac{t}{K}}.
Hence, charge on it will be Q′=Aϵ0Vd−t+tK{Q}^{'}=\dfrac{A{\epsilon }_{0}V}{d-t+\dfrac{t}{K}}
Given:
Aϵ0Vd−t+tK=(1.25)Aϵ0Vd\dfrac{A{\epsilon }_{0}V}{d-t+\dfrac{t}{K}}=\left(1.25\right)\dfrac{A{\epsilon }_{0}V}{d}
⇒1.25(3+2K)=5\Rightarrow 1.25\left(3+\dfrac{2}{K}\right)=5
⇒K=2\Rightarrow K=2

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