Determine a system of first-order differential equations that describes the currents i, (t) and i,(t) in the electrical network shown in the figure below. R1 L2 E R2 R3 2 + R,!3 = E di

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Determine a system of first-order differential equations that describes the currents i, (t) and i,(t) in the electrical network shown in the figure below.
ww
R1
E
L2
R2
R3
D2 + R,i3 = E
+
dt
dig
+ R,i2 +
dt
| )» = e
Transcribed Image Text:Determine a system of first-order differential equations that describes the currents i, (t) and i,(t) in the electrical network shown in the figure below. ww R1 E L2 R2 R3 D2 + R,i3 = E + dt dig + R,i2 + dt | )» = e
As shown in the figure below, a small metal bar is placed inside container A, and container A then is placed within a much larger container B.
container B
container A
metal
bar
TĄ (1)
TR = constant
As the metal bar cools, the ambient temperature T,(t) of the medium within container A changes according to Newton's law of cooling. As container A cools, the temperature of the medium inside container B
does not change significantly and can be considered to be a constant T.. Construct a mathematical model for the temperatures T(t) and T,(t), where T(t) is the temperature of the metal bar inside container A.
This model can be solved by using prior knowledge. (Use T for T(t) and T, for T,(t). Assume that the temperature of the metal does not affect the temperature of container A and both k, and k are constants.)
dT
dt
k <0
dT
k<0
=
dt
Find a solution of the system subject to the initial conditions T(0) = To, T(0) = T,.
T(t) =
Transcribed Image Text:As shown in the figure below, a small metal bar is placed inside container A, and container A then is placed within a much larger container B. container B container A metal bar TĄ (1) TR = constant As the metal bar cools, the ambient temperature T,(t) of the medium within container A changes according to Newton's law of cooling. As container A cools, the temperature of the medium inside container B does not change significantly and can be considered to be a constant T.. Construct a mathematical model for the temperatures T(t) and T,(t), where T(t) is the temperature of the metal bar inside container A. This model can be solved by using prior knowledge. (Use T for T(t) and T, for T,(t). Assume that the temperature of the metal does not affect the temperature of container A and both k, and k are constants.) dT dt k <0 dT k<0 = dt Find a solution of the system subject to the initial conditions T(0) = To, T(0) = T,. T(t) =
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