Exercise:
In a parallel plate capacitor with air between the plates, each plate has an area of $6 \times 10^{- 3} m^{2}$ and the distance between the plates is 3 mm. Calculate the capacitance of the capacitor. If this capacitor is connected to a 100 V supply, what is the charge on each plate of the capacitor?

Explain what would happen if in the capacitor given in Exercise a $3 m m$ thick mica sheet (of dielectric constant = 6) were inserted between the plates,
(a) While the voltage supply remained connected.
(b) After the supply was disconnected.

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Solution

$C = \frac{ϵ_{o} A}{d}$
According to the values given $C = 1.8 \times 10^{- 11} F$
Now $Q = C V$
Hence charge on the positive plate will be $1.8 \times 10^{- 9} C$
(a) Dielectric constant, k = 6
$C = 1.8 \times 10^{- 11} F$
new capacitance, $C^{'} = k C = 108 p F$
$V = 100 v o l t s$
$q^{'} = V \times C^{'} = 1.08 \times 10^{- 8} C$
V remains the same.

(b) $C^{'} = k C = 6 \times 1.8 \times 10^{- 11} = 108 p F$
q remains the same.
$q = 1.8 \times 10^{- 9} C$
$V^{'} = q / C^{'} = 16.67 V$

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Similar questions

Explain what would happen if in the capacitor given in Exercise 2.8, a 3 mm thick mica sheet (of dielectric constant = 6) were inserted between the plates,

(a) While the voltage supply remained connected.

(b) After the supply was disconnected.

Q. In a parallel plate capacitor with air between the plates each plate has an area of 5 × 10^-3 metre square and the separation between the plates is 2.5 millimetres.
Calculate the capacitance of the capacitor .
If this capacitor is connected to 100 volt supply what would be the charge on each plate.
How would the charge on the plate be affected if a 2.5 mm thick mica sheet of K equal to 8 is inserted between the plates while the voltage supply remains connected ?

Q. A parallel plate air capacitor with no dielectric between the plates is connected to the constant voltage source. What will be the new capacitance and charge on the capacitor if a dielectric with dielectric constant

K = 5

is inserted between the plates? Intially capacitance and charge on the capacitor are

50 μ F

and

200 μ C

respectively before the introduction of the dielectric.

Q. A parallel plate air capacitor with no dielectric between the plates is connected to the constant voltage source. How would capacitance and charge change if the dielectric constant

K = 2

is inserted between the plates ?

C_{0}

and

Q_{0}

are the capacitance and charge of the capacitor before the introduction of the dielectric.

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