A parallel plate air capacitor has a capacitance C. When it is half filled as shown in figure with a dielectric constant $K$ = 5, the percentage increase in the capacitance is ____. [2026]

Question

Smart Achievers · Accepted Answer

(2)

$Initial capacitance: C_{i} = \frac{A ε_{0}}{d} = C$

$Final capacitance:$

$C_{1} = \frac{A ε_{0} \times 5}{\frac{d}{2}} = 10 C and C_{2} = \frac{A ε_{0}}{\frac{d}{2}} = 2 C$

$C_{f} = \frac{C_{1} C_{2}}{C_{1} + C_{2}} = \frac{10 \times 2}{10 + 2} C = \frac{5}{3} C$

$% increase = \frac{\frac{5}{3} C - C}{C} \times 100 = 66.67$

Solution

Q.
A parallel plate air capacitor has a capacitance C. When it is half filled as shown in figure with a dielectric constant $K$ = 5, the percentage increase in the capacitance is ____. [2026]

1 33.34

2 66.67

3 200

4 400

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