28.38 In contrast to Prob. 28.37, real resistors may not always obey Ohm's law. For example, the voltage drop may be nonlinear and the circuit dynamics is described by a relationship such as di L + R dt where all other parameters are as defined in Prob. 28.37 and I is a known reference current equal to 1. Solve for i as a function of time under the same conditions as specified in Prob. 28.37.

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Ans 28.38

28.38 In contrast to Prob. 28.37, real resistors may not always obey
Ohm's law. For example, the voltage drop may be nonlinear and the
circuit dynamics is described by a relationship such as
di
+ R
dt
where all other parameters are as defined in Prob. 28.37 and I is a
known reference current equal to 1. Solve for i as a function of time
under the same conditions as specified in Prob. 28.37.
28.8 Compound A diffuses through a 4-cm-long tube and reacts as
it diffuses. The equation governing diffusion with reaction is
d²A
D-
dx
kA = 0
At one end of the tube, there is a large source of A at a concentra-
tion of 0.1 M. At the other end of the tube there is an adsorbent
material that quickly absorbs any A, making the concentration 0 M.
If D = 1.5 x 10 “ cm³/s and k= 5 × 10°s', what is the concen-
tration of A as a function of distance in the tube?
Use Euler, Heun, 2 order RK methods.
28.43 The rate of heat flow (conduction) between two points on a
cylinder heated at one end is given by
dQ
dT
dt
dx
where A = a constant, A = the cylinder's cross-sectional area,
Q = heat flow, T = temperature, † = time, and x = distance from
the heated end. Because the equation involves two derivatives, we
will simplify this equation by letting
dT 100(L – x)(20 – 1)
dx
100 - xt
where L is the length of the rod. Combine the two equations and
compute the heat flow for t = 0 to 25 s. The initial condition is
Q(0) = 0 and the parameters are A = 0.5 cal · cm/s, A = 12 cm²,
L = 20 cm, and x= 2.5 cm. Plot your results.
Use Euler, Heun, 2nd order RK methods.
Transcribed Image Text:28.38 In contrast to Prob. 28.37, real resistors may not always obey Ohm's law. For example, the voltage drop may be nonlinear and the circuit dynamics is described by a relationship such as di + R dt where all other parameters are as defined in Prob. 28.37 and I is a known reference current equal to 1. Solve for i as a function of time under the same conditions as specified in Prob. 28.37. 28.8 Compound A diffuses through a 4-cm-long tube and reacts as it diffuses. The equation governing diffusion with reaction is d²A D- dx kA = 0 At one end of the tube, there is a large source of A at a concentra- tion of 0.1 M. At the other end of the tube there is an adsorbent material that quickly absorbs any A, making the concentration 0 M. If D = 1.5 x 10 “ cm³/s and k= 5 × 10°s', what is the concen- tration of A as a function of distance in the tube? Use Euler, Heun, 2 order RK methods. 28.43 The rate of heat flow (conduction) between two points on a cylinder heated at one end is given by dQ dT dt dx where A = a constant, A = the cylinder's cross-sectional area, Q = heat flow, T = temperature, † = time, and x = distance from the heated end. Because the equation involves two derivatives, we will simplify this equation by letting dT 100(L – x)(20 – 1) dx 100 - xt where L is the length of the rod. Combine the two equations and compute the heat flow for t = 0 to 25 s. The initial condition is Q(0) = 0 and the parameters are A = 0.5 cal · cm/s, A = 12 cm², L = 20 cm, and x= 2.5 cm. Plot your results. Use Euler, Heun, 2nd order RK methods.
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