A sensitive electronic device of resistance `175Omega` is to be connected to a source of emf by a switch. The device is designed to operate with a current of `36mA` but to avoid damage to the device, the current can rise to no more than `4.9mA` in the first `58mus` after the switch the closed. To protect the device it is connected in series with an inductor.
a. What emf must the source have?
b. What inductance is required?
c. What is the time constant?

Explanation

a. Given `R=175Omega` and peak value current
`i_0=36xx10^-3A`
Applied voltage `V=i_0R=(175)(36xx10^-3)"volt"=6.3V`
b. From the relation
`i=i_0(1-e^(-t//tau_L))`
We have, `(4.9)=(36)[1-e^(-t//tau_L)]`
or `e^(-t//tau_L)=1-4.9/36=0.864`
`:. t/tau_L=ln(0.864)=0.146`
or `t/(L//R)=0.146`
`:. (Rt)/L=0.146`
or `L=(Rt)/0.146=((175)(58xx10^-6))/0.146`
`=7.0xx10^-2H`
c.Time constant of the circuit
`tau_L=L/R=(7.0xx10^-2)/175`
`=4.0xx10^-4`