A parallel-plate capacitor is formed by two plates, each of area 100 cm2 separated by a distance of 1 mm. A dielectric of dielectric constant 5.0 and dielectric strength 1.9×107Vm−1 is filled between the plates. Find the maximum charge that can be stored on the capacitor without causing any dielectric breakdown.

If Q be the charge on the capacitor, the surface charge density is σ=Q/A and the electric field is QKAε0 . This should not exceed the dielectric strength 1.9×107Vm−1. Thus, the maximum charge is given by QKAε0=1.9×107Vm−1Or, Q=KAε0×1.9×10−7Vm−1=(5.0)10−2m28.85×10−12Fm−1×1.9×107Vm−1=8.4×10−6C .

A parallel-plate capacitor is formed by two plates, each of area 100 cm2 separated by a distance of 1 mm. A dielectric of dielectric constant 5.0 and dielectric strength 1.9×107Vm−1 is filled between the plates. Find the maximum charge that can be stored on the capacitor without causing any dielectric breakdown.

If Q be the charge on the capacitor, the surface charge density is σ=Q/A and the electric field is QKAε0 . This should not exceed the dielectric strength 1.9×107Vm−1. Thus, the maximum charge is given by QKAε0=1.9×107Vm−1Or, Q=KAε0×1.9×10−7Vm−1=(5.0)10−2m28.85×10−12Fm−1×1.9×107Vm−1=8.4×10−6C .

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A parallel-plate capacitor is formed by two plates, each of area $100 {cm}^{2}$ separated by a distance of 1 mm. A dielectric of dielectric constant 5.0 and dielectric strength $1 .9 \times 10^{7} {Vm}^{- 1}$ is filled between the plates. Find the maximum charge that can be stored on the capacitor without causing any dielectric breakdown.

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$8 .4 \times 10^{- 6} C$

10 C

$9 \times 10^{- 6} C$

$11 \times 10^{- 6} C$

answer is A.

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Detailed Solution

If Q be the charge on the capacitor, the surface charge density is $σ = Q / A$

and the electric field is $\frac{Q}{{KAε}_{0}}$ .

This should not exceed the dielectric strength $1 .9 \times 10^{7} {Vm}^{- 1}$ .

Thus, the maximum charge is given by $\frac{Q}{{KAε}_{0}} = 1 .9 \times 10^{7} {Vm}^{- 1}$
Or, $Q = {KAε}_{0} \times 1 .9 \times 10^{- 7} {Vm}^{- 1}$
$= (5.0) (10^{- 2} m^{2}) (8.85 \times 10^{- 12} {Fm}^{- 1}) \times (1.9 \times 10^{7} {Vm}^{- 1}) = 8.4 \times 10^{- 6} C$
.