$\"\"$

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The generator supplies voltage is $\"\"$ .

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The inductance is $\"\"$ .

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The resistance is $\"\"$ .

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The initial condition is $\"\"$ .

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(a) Find $\"\"$ .

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From figure (4):

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The first order linear differential equation is $\"\"$ .

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

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$\"\"$ .

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The equation is in the form of $\"\"$ .

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The differential equation is a first order linear differential equation.

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Solution of the first order linear differential equation is $\"\"$ is $\"\"$ .

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Here $\"\"$ and $\"\"$ .

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Find $\"\"$ .

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$\"\"$

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$\"\"$ .

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$\"\"$ .

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The solution of differential equation is $\"\"$ .

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

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$\"\"$

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$\"\"$

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Apply integration by parts formula: $\"\"$ .

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Consider $\"\"$ and $\"\"$ .

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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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Substitute corresponding values in parts of integration formula.

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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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$\"\"$ .

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Substitute $\"\"$ .

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$\"\"$

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

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$\"\"$ .

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$\"\"$

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(b)

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Find the current after $\"\"$ .

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

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$ .

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$\"\"$

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(c)

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Graph the function $\"\"$ .

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$\"\"$

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$\"\"$

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(a) $\"\"$ .

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(b) $\"\"$ .

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(c)

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Graph of the function $\"\"$ .

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$\"\"$ .