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

Write the expression of current in terms of time.

Options

A. `i = i_0(t)/(t_0)`
B. `i= i_0(1+(t)/(t_0))`
C. `i=i_0((t)/(t_0) - 1)`
D. `I = i_0(1-(t)/(t_0))`

Answer

D

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)`