The electric current through a wire varies with time as I = I 0 + β t , where I 0 = 20 A and β = 3 A s - 1 . The amount of electric charge crossed through a section of the wire in 20 s is:

Step-by-step solution

Given that Current I = I 0 + β t , I 0 = 20 A and β = 3 A s - 1 The instantaneous current is given by I = 20 + 3 t . . . 1 Integrating equation (1), we have d q d t = 20 + 3 t ⇒ ∫ 0 q d q = ∫ 0 20 ( 20 + 3 t ) d t ⇒ q = ∫ 0 20 20 d t + ∫ 0 20 3 t d t ⇒ q = 20 t + 3 t 2 2 0 20 = 1000 C