A precision Labratory resistor is made of a coil of wire with 500 turns that wit

Question

A precision Labratory resistor is made of a coil of wire with 500 turns that with a diameter of 1.50 cm that is 4.00 cm long. A. What is the resistors self inductance? B. What average emf is induced in the resistor if a 12.0A current through it is turned on in 5.00ms? C. If the wire used to make the resistor has a resistance of 1.00 ohms per meter, what is the resistors resistance? D. What is its inductance if it is shortened to half its length and counter wound (two layers of 250 turns in opposite directions)? A precision Labratory resistor is made of a coil of wire with 500 turns that with a diameter of 1.50 cm that is 4.00 cm long. A. What is the resistors self inductance? B. What average emf is induced in the resistor if a 12.0A current through it is turned on in 5.00ms? C. If the wire used to make the resistor has a resistance of 1.00 ohms per meter, what is the resistors resistance? D. What is its inductance if it is shortened to half its length and counter wound (two layers of 250 turns in opposite directions)? A. What is the resistors self inductance? B. What average emf is induced in the resistor if a 12.0A current through it is turned on in 5.00ms? C. If the wire used to make the resistor has a resistance of 1.00 ohms per meter, what is the resistors resistance? D. What is its inductance if it is shortened to half its length and counter wound (two layers of 250 turns in opposite directions)?

Explanation / Answer

A)
given,

d = 1.5 cm = 0.015 m

l = 4 cm = 0.04 m

self inductance of solenoid, L = mue*N^2*A/l

= 4*pi*10^-7*500^2*(pi*0.015^2/4)/0.04

= 1.39*10^-3 H
B)

Average induced emf = L*dI/dt

= 1.39*10^-3*12/(5*10^-3)

= 3.336 volts

C) total length of the wire = N*pi*d

= 500*pi*0.014

= 21.99 m

so, total resiatnce of the wire, R = 21.99*1 = 21.99 ohm

D) N = 250 turns

l = 4/2 = 2 cm = 0.02 m

self inductance, L = L = mue*N^2*A/l

= 4*pi*10^-7*250^2*(pi*0.015^2/4)/0.02

= 6.94*10^-4 H

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