Acoil with a self-inductance of 3.0 h and a resistance of 100ω carries a steady current of 2.0 a. (a) what is the energy stored in the magnetic field of the coil? (b) what is the energy per second dissipated in the resistance of the coil?

energy stored in the magnetic field of coil is 6 J

energy per second dissipated in the resistance of the coil is 400 W

Explanation:

Given data

inductance = 3.0 H

resistance = 100Ω

current = 2.0 A

to find out

energy stored in the magnetic field  and  energy per second dissipated

solution

we know that energy stored in the magnetic field is express as

E = 1/2 × L×I²

here  E is energy store and L is inductance and I is current

put all value we get

E = 1/2 × L×I²

E = 1/2 × 3 ×2²

E  = 6 J

energy stored in the magnetic field of coil is 6 J

and

energy per second is power

so power = I²×R

power = 2² × 100

power = 400 W

so energy per second dissipated in the resistance of the coil is 400 W

the minimum constant speed at which she can catch the train is 2.7 m/s

given:

acceleration = 0.6

time = 4.5 s

to find:

velocity = ?

formula used:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

solution:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

v = 0 + (0.6 × 4.5)

v = 2.7 m/s

the minimum constant speed at which she can catch the train is 2.7 m/s