A parallel plate capacitor having capacitance

Question:

A parallel plate capacitor having capacitance $12 \mathrm{pF}$ is changed by a battery to a potential difference of $10 \mathrm{~V}$ between its plates. The charging battery is now disconnected and a porcelain slab of dielectric constant $6.5$ is slipped between the plates. The work done by the capacitor on the slab is:

  1. (1) $692 \mathrm{pJ}$

  2. (2) $508 \mathrm{pJ}$

  3.  (3) $560 \mathrm{pJ}$

  4. (4) $600 \mathrm{pJ}$


Correct Option: , 2

Solution:

(2) $\mathrm{W}=-\Delta \mathrm{u}$

$=(-1)\left|\frac{(c \varepsilon)^{2}}{2 k c}-\frac{(c \varepsilon)^{2}}{2 c}\right|$

$=\frac{\varepsilon^{2} c}{2} \frac{k-1}{k}$

$=508 \mathrm{~J}$

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