$\"\"$

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The electromotive force is $\"\"$ , where $\"\"$ is capacitance in farads, $\"\"$ is resistance in ohms, $\"\"$ is charge in coulombs.

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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Substitute $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Apply integral on each side.

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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The initial condition is $\"\"$ when $\"\"$ .

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Substitute $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$ .

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The limiting value of charge is $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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The limiting value of the charge is $\"\"$ .

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$\"\"$

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$\"\"$ .

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The limiting value of the charge is $\"\"$ .