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The current through a wire varies with t...

The current through a wire varies with time as `I = I_(0) + alpha t `, where `I_(0) = 10` A and `alpha = 4 As^(-1)` . The charge that flows across a cross-section of the wire in first 10 seconds is .....

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Current , I = `(dq)/(dt) = I_(0) + alpha t `
`therefore dq = (I_(0) + alpha t ) dt `
Integrating on both sides,
` Q = int dq = int_(t = 0)^(t = 10 ) (I_(0) + alpha t) dt `
`= int_(0)^(10) l_(0)" dt " + int_(0)^(10) alpha` t dt
`= I_(0) int_(0)^(10) dt + alpha int_(0)^(10) ` t dt
= `I_(0) [ t]_(0)^(10) + alpha [ (t^(2))/(2) ]_(0)^(10)`
` = 10I_(0) + 50 alpha `
Substituting ` I_(0) = 10 and alpha = 4 `
Q = 10 (10 ) + 50(4) = 300 C
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