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The current through a wire varies with time asI = 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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Answer» SOLUTION :Current , I = `(dq)/(dt) = I_(0) + ALPHA t ` `thereforedq= (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 + alphaint_(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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