The charge supplied by a battery to a cylindrical capacitor of coaxial cylinders of radii $4 c m$ and $6 c m$ with length $1 m$ to charge it to a potential of $4 k V$ is:

0.429 μ C

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0.548 μ C

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0.628 μ C

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0.889 μ C

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Solution

The correct option is B $0.548 μ C$

If the capacitor is in the form of two conducting coaxial cylinders of radii $r_{1}$ & $r_{2} (r_{1} < r_{2})$ and length L, then the capacitance is $C = \frac{2 π ϵ L}{l n \frac{r_{2}}{r_{1}}}$ where $ϵ$ is the permittivity of the material filling the gap between the cylinders.

So the charge, $Q = C V = \frac{2 π ϵ L}{l n \frac{r_{2}}{r_{1}}} V$

here, $r_{1} = 4 c m, r_{2} = 6 c m, L = 1 m, V = 4 k i l o v o l t, ϵ = 8.85 \times 10^{- 12}$ for air.

$∴ Q = \frac{2 \times 3.14 \times 8.85 \times 10^{- 12}}{l n \frac{6}{4}} \times 4 \times 10^{3} = 0.548 μ C$

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The charge supplied by a battery to a cylindrical capacitor of coaxial cylinders of radii 4cm and 6cm with length 1m to charge it to a potential of 4kV is:

The charge supplied by a battery to a cylindrical capacitor of coaxial cylinders of radii $4 c m$ and $6 c m$ with length $1 m$ to charge it to a potential of $4 k V$ is: