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Question 25.40: An air-filled parallel-plate capacitor has a capacitance of ......

An air-filled parallel-plate capacitor has a capacitance of 1.3 pF. The separation of the plates is doubled, and wax is inserted between them. The new capacitance is 2.6 pF. Find the dielectric constant of the wax.

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If the original capacitance is given by C=\varepsilon_0 A / d , then the new capacitance is C^{\prime}=\varepsilon_0 \kappa A / 2 d .Thus C^{\prime} / C=\kappa / 2 or

\kappa=2 C^{\prime} / C=2(2.6\, pF / 1.3 \,pF )=4.0 .

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