First slide

Capacitance

Question

A parallel plate capacitor with air between the plates has a 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 $k_{1} = 3$ and thickness d/3 while the other one has dielectric constant $k_{2} = 6$ and thickness 2d/3. Capacitance of the capacitor is now :

Moderate

A

20.25 pF
B

1.8 pF
C

45 pF
D

40.5 pF

Solution

Given C = $\frac{{Aε}_{0}}{d} = 9 pF$
Now, $C' = \frac{{Aε}_{0}}{\frac{d / 3}{k_{1}} + \frac{2 d / 3}{k_{2}}} = \frac{9}{2} \frac{{Aε}_{0}}{d} = \frac{81}{2} pF$

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