Answer:
The stored energy is 140.7 watt.
The thermal energy is 62.7 watt.
The delivered energy is 203.4 watt.
Explanation:
Given that,
Inductance = 2.8 H
Resistance = 12 Ω
Potential ![\epsilon_{0}=89\ V](https://tex.z-dn.net/?f=%5Cepsilon_%7B0%7D%3D89%5C%20V)
Time = 0.086 s
(a). We need to calculate the energy stored in the magnetic field
Using formula of current
![i=i_{max}(1-e^(\frac{-t}{\tau}))](https://tex.z-dn.net/?f=i%3Di_%7Bmax%7D%281-e%5E%28%5Cfrac%7B-t%7D%7B%5Ctau%7D%29%29)
Using formula of energy
![U=\dfrac{1}{2}Li^2](https://tex.z-dn.net/?f=U%3D%5Cdfrac%7B1%7D%7B2%7DLi%5E2)
On differentiating
![\dfrac{dU}{dt}=Li\frac{di}{dt}](https://tex.z-dn.net/?f=%5Cdfrac%7BdU%7D%7Bdt%7D%3DLi%5Cfrac%7Bdi%7D%7Bdt%7D)
![\dfrac{dU}{dt}=L\dfrac{d}{dt}(i_{max}(1-e^(\frac{-t}{\tau}))](https://tex.z-dn.net/?f=%5Cdfrac%7BdU%7D%7Bdt%7D%3DL%5Cdfrac%7Bd%7D%7Bdt%7D%28i_%7Bmax%7D%281-e%5E%28%5Cfrac%7B-t%7D%7B%5Ctau%7D%29%29)
Again differentiating
![\dfrac{dU}{dt}=\dfrac{\epsilon^2}{R}(1-e^{\frac{-t}{\tau}})e^{\frac{-t}{\tau}}](https://tex.z-dn.net/?f=%5Cdfrac%7BdU%7D%7Bdt%7D%3D%5Cdfrac%7B%5Cepsilon%5E2%7D%7BR%7D%281-e%5E%7B%5Cfrac%7B-t%7D%7B%5Ctau%7D%7D%29e%5E%7B%5Cfrac%7B-t%7D%7B%5Ctau%7D%7D)
![\dfrac{dU}{dt}=\dfrac{\epsilon^2}{R}(1-e^{\frac{-\t\times R}{L}})e^{\frac{-t\times R}{L}}](https://tex.z-dn.net/?f=%5Cdfrac%7BdU%7D%7Bdt%7D%3D%5Cdfrac%7B%5Cepsilon%5E2%7D%7BR%7D%281-e%5E%7B%5Cfrac%7B-%5Ct%5Ctimes%20R%7D%7BL%7D%7D%29e%5E%7B%5Cfrac%7B-t%5Ctimes%20R%7D%7BL%7D%7D)
Put the value into the formula
![\dfrac{dU}{dt}=\dfrac{(89)^2}{12}(1-e^{\dfrac{-0.086\times12}{2.8}})e^{\dfrac{-0.086\times12}{2.8}}](https://tex.z-dn.net/?f=%5Cdfrac%7BdU%7D%7Bdt%7D%3D%5Cdfrac%7B%2889%29%5E2%7D%7B12%7D%281-e%5E%7B%5Cdfrac%7B-0.086%5Ctimes12%7D%7B2.8%7D%7D%29e%5E%7B%5Cdfrac%7B-0.086%5Ctimes12%7D%7B2.8%7D%7D)
![\dfrac{dU}{dt}=140.7\ watt](https://tex.z-dn.net/?f=%5Cdfrac%7BdU%7D%7Bdt%7D%3D140.7%5C%20watt)
(b). We need to calculate the thermal energy
Using formula of thermal energy
![P=i^2R](https://tex.z-dn.net/?f=P%3Di%5E2R)
![P=\dfrac{\epsilon^2}{R}(1-e^{\frac{-t}{\tau}})^2](https://tex.z-dn.net/?f=P%3D%5Cdfrac%7B%5Cepsilon%5E2%7D%7BR%7D%281-e%5E%7B%5Cfrac%7B-t%7D%7B%5Ctau%7D%7D%29%5E2)
Put the value into the formula
![P=\dfrac{89^2}{12}(1-e^{\dfrac{-0.086\times12}{2.8}})^2](https://tex.z-dn.net/?f=P%3D%5Cdfrac%7B89%5E2%7D%7B12%7D%281-e%5E%7B%5Cdfrac%7B-0.086%5Ctimes12%7D%7B2.8%7D%7D%29%5E2)
![P=62.7\ Watt](https://tex.z-dn.net/?f=P%3D62.7%5C%20Watt)
(c). We need to calculate the delivered energy by the battery
Using formula of energy
![P'=P+\dfrac{dU}{dt}](https://tex.z-dn.net/?f=P%27%3DP%2B%5Cdfrac%7BdU%7D%7Bdt%7D)
![P'=62.7+140.7](https://tex.z-dn.net/?f=P%27%3D62.7%2B140.7)
![P'=203.4\ watt](https://tex.z-dn.net/?f=P%27%3D203.4%5C%20watt)
Hence, The stored energy is 140.7 watt.
The thermal energy is 62.7 watt.
The delivered energy is 203.4 watt.
Because the gas weighs more than the tubes thus causing them to spin
The various points on the heating curve corresponds to melting, boiling and vaporization.
<h3>Heating curve</h3>
A heating curve is a plot of temperature against time. The heating curve reveals how the temperature of the body changes with time during heating.
The heating curve is not shown here hence the question is incomplete. However, we must note that The various points on the heating curve corresponds to melting, boiling and vaporization.
Learn more about heating curve: brainly.com/question/10481356
I think 14 maybe 234567 but im not sure