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The current through a wire varies with time as I= I_(0) + alpha t , where I_(0)= 1A and alpha =4 As^(-1) . The charge that flows across a cross-section or the wire In first 10 seconds is .... |
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Answer» 210 C 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) I_(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)` `= 10 I_(0) + 50 alpha ` Substituting `I_(0) = 10 and alpha = 4 ` Q = 10 (10) + 50 (4) 300 C |
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