The current through a wire varies wilh time as I = `I_(0) + alpha `t where `I_(0) ` = 20 A and `alpha = 3 A s^(-1)` . Find the charge that flows across a cross - section of the wire in first 10 seconds.

Options

A. 350 C
B. 300 C
C. 200 C
D. 150 C

Answer

A

Explanation

350 C
Q = `int_(0)^(10) I dt = int_(0)^(10) ( I_(0) + alpha t) dt = int_(0)^(10) ( 20 + 3t) dt `
`therefore Q = [ 20 t + (3t^(2))/(2) ]_(0)^(10)`
` therefore Q = [ 20 xx 10 + (3 xx 100)/(2) ] `
`therefore Q = [ 200 + 150]`
`therefore Q = 350 C `