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Physics · Electrostatic Potential
हिन्दीA parallel plate capacitor with plate area \( A \) and plate separation \( d \) is filled with a dielectric slab of dielectric constant \( K = 4 \) and thickness \( t = \frac{2}{3}d \). If the original capacitance without dielectric is \( C_0 \), what is the new capacitance of the system?
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Correct answer · Option B
\( 2 C_0 \)
Explanation
The capacitance with dielectric slab of thickness \( t \) is \( C = \frac{\varepsilon_0 A}{d - t + \frac{t}{K}} = \frac{C_0}{1 - \frac{t}{d}(1 - \frac{1}{K})} \). For \( t = \frac{2}{3}d \) and \( K = 4 \), \( C = \frac{C_0}{1 - \frac{2}{3}(1 - \frac{1}{4})} = \frac{C_0}{1 - \frac{1}{2}} = 2C_0 \).
