An inductor of `2` henry and a resistance of `10` ohms are connected in series with a battery of `5` volts. The initial rate of change of current is

Options

A. `0.5 amp//sec`
B. `2.0 amp//sec`
C. `2.5 amp//sec`
D. `0.25 amp//sec`

Answer

C

Explanation

`i=i_(0)(1-e^(-Rt)/(L))implies(di)/(dt)=(d)/(dt)i_())-(d)/((dt)i_(0)e^(-Rt)/(L)`
`implies(di)/(dt)=0-i0(-(R )/(L))e^(-(Rt)/(L)=(i_(0)R)/(L)e^(-Rt)/(L)`
initially, `t=0implies(di)/(dt)=(i_(0)xxR)/(L)=(E)/(L)=(5)/(2)=2.5 amp//sec`.