$\"\"$

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The battery supplies a constant 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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$\"\"$

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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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Substitute $\"\"$ .

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$\"\"$

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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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(b) 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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$\"\"$

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(a) $\"\"$ .

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(b) $\"\"$ .