Relation between current in a conductor and time is shown in fig.

Total charge flowing through the conductor is

Options

A. `i_(0)t_(0)//2`
B. `i_(0)t_(0)`
C. `i_(0)t_(0)//4`
D. `2i_(0)t_(0)`

Answer

A

Explanation

`q = int idt =` area of given curve `= (1)/(2)i_0t_0`
`(i)/(i_0) +(t)/(t_0) 1` or `I = i_0(1-(t)/(t_0))`
Heat `= int i^2 Rdt = int_0^(t_0)i_0^2R(1-(t)/(t_0))^2 dt`
`H = (i_0^2R(1-(t)/(t_0))^3)/(3(-(1)/(t_0)))]_0^(t0) or H = (Rt_0i_0^2)/(3)`