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Question: The capacitance of an air capacitor is \(15 \mu F\)the separation between the parallel plates is![](...

The capacitance of an air capacitor is 15μF15 \mu Fthe separation between the parallel plates is. A copper plate of thickness is introduced symmetrically between the plates. The capacitance now becomes

A

5μF5 \mu F

B

7.5μF7.5 \mu F

C

22.5μF22.5 \mu F

D

30μF30 \mu F

Answer

30μF30 \mu F

Explanation

Solution

By using Cair=ε0AdC _ { a i r } = \frac { \varepsilon _ { 0 } A } { d } Cmedium =ε0Ad−t+tKC _ { \text {medium } } = \frac { \varepsilon _ { 0 } A } { d - t + \frac { t } { K } }

For K = ∞ Cmedium =ε0Ad−tC _ { \text {medium } } = \frac { \varepsilon _ { 0 } A } { d - t }

⇒ Cm15=66−3\frac { C _ { m } } { 15 } = \frac { 6 } { 6 - 3 } ⇒ Cm=30μCC _ { m } = 30 \mu \mathrm { C }