Given Information:
Inductance = L = 5 mH = 0.005 H
Time = t = 2 seconds
Required Information:
Current at t = 2 seconds = i(t) = ?
Energy at t = 2 seconds = W = ?
Answer:
Current at t = 2 seconds = i(t) = 735.75 A
Energy at t = 2 seconds = W = 1353.32 J
Explanation:
The voltage across an inductor is given as
![V(t) = 5(1-e^{-0.5t})](https://tex.z-dn.net/?f=V%28t%29%20%3D%205%281-e%5E%7B-0.5t%7D%29)
The current flowing through the inductor is given by
![i(t) = \frac{1}{L} \int_0^t \mathrm{V(t)}\,\mathrm{d}t \,+ i(0)](https://tex.z-dn.net/?f=i%28t%29%20%3D%20%5Cfrac%7B1%7D%7BL%7D%20%5Cint_0%5Et%20%5Cmathrm%7BV%28t%29%7D%5C%2C%5Cmathrm%7Bd%7Dt%20%5C%2C%2B%20i%280%29)
Where L is the inductance and i(0) is the initial current in the inductor which we will assume to be zero since it is not given.
![i(t) = \frac{1}{0.005} \int_0^t \mathrm{5(1-e^{-0.5t}}) \,\mathrm{d}t \,+ 0\\\\i(t) = 200 \int_0^t \mathrm{5(1-e^{-0.5t}}) \,\mathrm{d}t \\\\i(t) = 200 \: [ {5\: (t + \frac{e^{-0.5t}}{0.5})]_0^t \\i(t) = 200\times5\: \: [ { (t + 2e^{-0.5t} + 2 )] \\](https://tex.z-dn.net/?f=i%28t%29%20%3D%20%5Cfrac%7B1%7D%7B0.005%7D%20%5Cint_0%5Et%20%5Cmathrm%7B5%281-e%5E%7B-0.5t%7D%7D%29%20%5C%2C%5Cmathrm%7Bd%7Dt%20%5C%2C%2B%200%5C%5C%5C%5Ci%28t%29%20%3D%20200%20%5Cint_0%5Et%20%5Cmathrm%7B5%281-e%5E%7B-0.5t%7D%7D%29%20%5C%2C%5Cmathrm%7Bd%7Dt%20%5C%5C%5C%5Ci%28t%29%20%3D%20200%20%5C%3A%20%5B%20%7B5%5C%3A%20%28t%20%2B%20%5Cfrac%7Be%5E%7B-0.5t%7D%7D%7B0.5%7D%29%5D_0%5Et%20%5C%5Ci%28t%29%20%3D%20200%5Ctimes5%5C%3A%20%5C%3A%20%5B%20%7B%20%28t%20%2B%202e%5E%7B-0.5t%7D%20%2B%202%20%29%5D%20%5C%5C)
![i(t) = 1000t +2000e^{-0.5t} -2000\\](https://tex.z-dn.net/?f=i%28t%29%20%3D%201000t%20%2B2000e%5E%7B-0.5t%7D%20-2000%5C%5C)
So the current at t = 2 seconds is
![i(t) = 1000(2) +2000e^{-0.5(2)} -2000\\\\i(t) = 735.75 \: A](https://tex.z-dn.net/?f=i%28t%29%20%3D%201000%282%29%20%2B2000e%5E%7B-0.5%282%29%7D%20-2000%5C%5C%5C%5Ci%28t%29%20%3D%20735.75%20%5C%3A%20A)
The energy stored in the inductor at t = 2 seconds is
![W = \frac{1}{2}Li(t)^{2}\\\\W = \frac{1}{2}0.005(735.75)^{2}\\\\W = 1353.32 \:J](https://tex.z-dn.net/?f=W%20%3D%20%5Cfrac%7B1%7D%7B2%7DLi%28t%29%5E%7B2%7D%5C%5C%5C%5CW%20%3D%20%5Cfrac%7B1%7D%7B2%7D0.005%28735.75%29%5E%7B2%7D%5C%5C%5C%5CW%20%3D%201353.32%20%5C%3AJ)
The claim being made in in the above passage is that " It makes financial sense to stop using the penny." (Option B)
<h3>
What textual evidence backs up the above claim?</h3>
The textual evidence that supports the above claim is "Not only does it make financial sense to take the penny out of circulation, but it also makes environmental sense." [Para. 2]
Textual evidence is evidence related to a text which supports claims made in such a text.
Learn more about claims at:
brainly.com/question/2748145
#SPJ1
Answer:64.10 Btu/lbm
Explanation:
Work done in an isothermally compressed steady flow device is expressed as
Work done = P₁V₁ In { P₁/ P₂}
Work done=RT In { P₁/ P₂}
where P₁=13 psia
P₂= 80 psia
Temperature =°F Temperature is convert to °R
T(°R) = T(°F) + 459.67
T(°R) = 55°F+ 459.67
=514.67T(°R)
According to the properties of molar gas, gas constant and critical properties table, R which s the gas constant of air is given as 0.06855 Btu/lbm
Work = RT In { P₁/ P₂}
0.06855 x 514.67 In { 13/ 80}
=0.06855 x 514.67 In {0.1625}
= 0.06855 x 514.67 x -1.817
=- 64.10Btu/lbm
The required work therefore for this isothermal compression is 64.10 Btu/lbm
Answer:
The maximum water pressure at the discharge of the pump (exit) = 496 kPa
Explanation:
The equation expressing the relationship of the power input of a pump can be computed as:
![E _{pump,u} = \dfrac{m(P_2-P_1)}{\rho}](https://tex.z-dn.net/?f=E%20_%7Bpump%2Cu%7D%20%3D%20%5Cdfrac%7Bm%28P_2-P_1%29%7D%7B%5Crho%7D)
where;
m = mass flow rate = 120 kg/min
the pressure at the inlet
= 96 kPa
the pressure at the exit
= ???
the pressure
= 1000 kg/m³
∴
![0.8 \times 10^{3} \ W = \dfrac{(120 \ kg/min * 1min/60 s)(P_2-96000)}{1000}](https://tex.z-dn.net/?f=0.8%20%5Ctimes%2010%5E%7B3%7D%20%5C%20W%20%3D%20%5Cdfrac%7B%28120%20%5C%20kg%2Fmin%20%2A%201min%2F60%20s%29%28P_2-96000%29%7D%7B1000%7D)
![0.8 \times 10^{3}\times 1000 = {(120 \ kg/min * 1min/60 s)(P_2-96000)}](https://tex.z-dn.net/?f=0.8%20%5Ctimes%2010%5E%7B3%7D%5Ctimes%201000%20%3D%20%7B%28120%20%5C%20kg%2Fmin%20%2A%201min%2F60%20s%29%28P_2-96000%29%7D)
![800000 = {(120 \ kg/min * 1min/60 s)(P_2-96000)}](https://tex.z-dn.net/?f=800000%20%3D%20%7B%28120%20%5C%20kg%2Fmin%20%2A%201min%2F60%20s%29%28P_2-96000%29%7D)
![\dfrac{800000}{2} = P_2-96000](https://tex.z-dn.net/?f=%5Cdfrac%7B800000%7D%7B2%7D%20%3D%20P_2-96000)
400000 = P₂ - 96000
400000 + 96000 = P₂
P₂ = 496000 Pa
P₂ = 496 kPa
Thus, the maximum water pressure at the discharge of the pump (exit) = 496 kPa