Question

2. You want to turn on the current through an inductor (inductance = L) in a controlled manner, so you place it in series with a resistor R = 2200 Ω, a switch, and a dc voltage source V0 = 240 V. After closing the switch, you find that the current through the coil builds up to its steady-state value with a time constant τ. You are pleased with the current’s steady-state value, but want τ to be half as long. a) What new values should you use for R and V0? b) After a time t = 2τ, how much energy is stored in the Inductor?

Answer 1

Given is:-

Now

part - a

The time constant is given by  

to make time constant half we have to make the resistance double, therefore the new resistance is

by plugging the values we get

which gives us

The current is given by  

Now the resistance is doubled but we want the current to be same as old value then we have to double up the voltage, therefore

by plugging the value we get

which gives us

Part - b

The current in the ckt is given by

Inductance of the ckt is = L

then the energy store in the inductor is given by

or

which gives us