If a current `I=4pi sin pi t` ampere flows through a wire, then find the amount of charge that flows through the wire in (i) t=0 to t=1s and (ii) t=1 s to t=2s.

Explanation

`Q=int_(t_1)^(t_2)Idt=4piint_(t_1)^(t2)sinpitdt=4pi[-(cospit)/pi]_(t_1)^(t_2)`
`=4(cos pit_1-cospit_2)`
(i) In this case ,t=0 and `t_2=1s`
Therefore, `Q_1=4(cos0-cospi)=4[1-(-1)]=8c`
(ii) In this case, `t_1=1s` and `t_2=2s`
Therefore `Q_2=4(cospi-cos2pi)=4[-1-1]=-8c`