Question

1. A solenoid having an inductance of 7.65 μH is connected in series with a 1.08 kΩ resistor. (a) If a 18.0 V battery is connected across the pair, how long will it take in seconds for the current through the resistor to reach 70.9% of its final value? (b) What is the current through the resistor at a time t = 1.00τL?

2.

A solenoid that is 70.9 cm long has a cross-sectional area of 21.1 cm². There are 921 turns of wire carrying a current of 8.75 A. (a) Calculate the energy density of the magnetic field inside the solenoid. (b) Find the total energy in joules stored in the magnetic field there (neglect end effects).

Answer 1

Problem - 1

Given is:-

Inductance  

Resistance

Now,

the time constant is given by

by plugging the values we get

which gives us

Part - a

voltage  

from RL circuit

current

by plugging the values we get

or

by taking both sides natural log we get

which gives us

Part - b

Time  

current is given by

by plugging the value of time t

or

which gives us

or