Homework Help: Energy absorbed by the inductor in 4 seconds

1. Dec 18, 2017

jaus tail

1. The problem statement, all variables and given/known data

2. Relevant equations
V = L di/dt
Energy = V*I*t

3. The attempt at a solution
First we find out V across L
This V will be there only for 1st 2 seconds as after that there is no change in current.
So V(across L) is L * di/dt = 2 * 6/2 = 6V equation 1
Now Current is a function of time so it's i = 3t equation 2
So to get Energy we use integration.
Energy = integration of V*I*dt where limits are 0 to 2
So now using equation 1 and 2 we get
Energy = integration of 6 * 3t dt from limits 0 to 2
so this is 18 t2/2 t varies from 0 to 2
So this is 9 (4) = 36 which is not in the options.
Where am I wrong.
I even tried other formula of Energy = 1/2 * L * I2 But this gives 24
I'm getting different answer for different formula but neither answer matches options. Where am I wrong?

2. Dec 18, 2017

Staff: Mentor

I don't see where you've taken into account the resistance of the inductor. Sure, the inductor won't be storing the energy lost to heat via the resistance, but it's energy absorbed (and then dissipated) by the inductor nonetheless.

I note that you didn't include the general formula for energy stored in an inductor in your relevant equations. It might prove handy in this instance

3. Dec 18, 2017

Windadct

The question is a little ambiguous - but I do think they are looking for total energy, Inductance (stored) and Resistance ( dissipated)

4. Dec 18, 2017

jaus tail

Book says answer is C
But I dont know how they got that. Power in inductor is 1/2 * L * i2
Why do I have to include resistance? The current is given. So current through inductor is known.

W = 1/2 L*i*i
Energy is integrating W*dt as t varies from 0 to time asked in question.

5. Dec 18, 2017

Staff: Mentor

The inductor, as a real component, has both inductance and resistance due to the resistivity of the coil of wire that it is made from. That wire resistance will dissipate energy in addition to the energy that the inductance will store in its magnetic field.

6. Dec 19, 2017

jaus tail

Oh okay. So I'll have to integrate i2R with respect to dt as t varies from 0 to 4 as well. Got it. Thanks.
That gives Energy across L as 36
Energy across R for transient time is 24
Energy across R in steady state is 72
Adding all I get answer as a)
Thanks.

7. Dec 19, 2017

Windadct

Also -- in this question the current is "set", formally defined -- normally (in a real case) both the inductor and the resistance would be impacting the total current and you would be seeing the impact of both elements more clearly..

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