An emf of 20 V is applied at time t = 0 to a circuit containing in series 10 mH inductor and 5`Omega` resistor. The ratio of the currents at time t = `oo` and t = 40 s is close to (take `e^2` = 7.389)

Options

A. 1.06
B. 1.48
C. 1.15
D. 0.84

Answer

A

Explanation

`=4(1-e^(-500t))`
`rArr` At `t=oo [("infinite"),(because e=e)]`
i=4(1-e)
`i_0=4A`

`i_0=4A`
`rArr` At t=40 s
`i_(40) = 4(1-e^(-500xx40))`
`=4(1-1/((e^2)^10000))`
`=4(1-1/((7.29)^10000))`
`i_0/i_40 = 1/(1(1/((7.29)^10000)))`
=1.06