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A parallel plate capacitor with air between the plates has capacitance of 9 pF. The separation between its plates is ‘d’. The space between the plates is now filled with two dielectrics. One of the dielectrics has dielectric constant k1 = 3 and thickness d/3 while the other one has dielectric constant k2 = 6 and thickness 2d/3. Capacitance of the capacitor is now

1. 1.8 pF
2. 45 pF
3. 40.5 pF
4. 20.25 pF

Correct answer: 40.5 pF

Solution

The capacitance of a capacitor filled with multiple dielectrics can be calculated by treating each dielectric as a separate capacitor in series. The effective capacitance is determined by the formula for capacitors in series, which results in a total capacitance of 40.5 pF when considering the contributions from both dielectrics with their respective dielectric constants and thicknesses.

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