Imagine that you want to wind a solenoid that can keep a 13-Ohm lightbulb lit lo
ID: 2238397 • Letter: I
Question
Imagine that you want to wind a solenoid that can keep a 13-Ohm lightbulb lit longer than 1 s after the circuit shown in figure E14.4b is disconnected from the battery (the bulb replaces the resistor in that circuit). If the form around which you wrap the coil has a radius of 6 cm. and you can wrap 1900 turns of superconducting (zero-resistance) wire around each linear meter of the form, how long will you have to make the form? Will this solenoid be approximately infinite (in the sense that its length is much greater than its radius)? Figure E14.4 (a) A solenoid coil connected in parallel to a resistor and a battery. After the circuit settles down to a steady state, the solenoid conducts a steady current l0. (b) If the battery is disconnected at t = 0, an emf will be induced in the solenoid that will continue to drive current through the resistor for a while.Explanation / Answer
L = uN^2A/l
time constant = L/R = uN^2A/lR
so, as per the specifications of the question,
5*L/R = 5uN^2A/lR = 1
so, l = 5uN^2A/R = 5*1.26*10^-6*1900^2*3.14*0.06^2/13 = 0.0198 m <-----length of the solenoid
AS the length is not longer than the radius the solenoid is not infinite......