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, t

Question

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 ____.

TestHub · Accepted Answer

Without dielectric, capacitance will be $C = \frac{A ε_{0}}{d}$ .

Therefore, charge on it, $Q = \frac{A ε_{0}}{d} V$

Now, with dielectric capacitance will be $C^{'} = \frac{A ε_{0}}{d - t + \frac{t}{K}}$ .

Hence, charge on it will be $Q^{'} = \frac{A ε_{0} V}{d - t + \frac{t}{K}}$

Given:

$\frac{A ε_{0} V}{d - t + \frac{t}{K}} = (1.25) \frac{A ε_{0} V}{d}$

$\Rightarrow 1.25 (3 + \frac{2}{K}) = 5$

$\Rightarrow K = 2$

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