OK doing it with the substitutions:
k = \frac{hA}{m_{Hg}C_{p,Hg}}
and
T = T_{Hg}
\frac{dT}{dt} = k(T_a - T)
\frac{1}{k(T_a - T)}dT = dt
\frac{-1}{k}\int\frac{1}{(-T_a + T)}dT = \int dt
\frac{-1}{k}ln|-T_a + T| = t + c
ln|-T_a + T| = -kt + c
-T_a + T = e^{-kt + c}
T = ce^{-kt} + T_a...
Homework Statement
I haven't done ODEs in a few years and I am trying to do this equation:
m_{Hg}C_{p,Hg}\frac{dT_{Hg}}{dt} = Q
Q = hA(T_{air} - T_{Hg})
T_{Hg}(t = 0) = 20
I need to find T_{Hg}(t=590)
Homework Equations
The Attempt at a Solution
h, A, m_{Hg}, C_{p,Hg}...
I updated the previous post but it must have happened after you replied:
Iref = 100uA
R = 43K
\frac{dIref}{dT} = \frac{1}{R}\frac{dR}{dT}(Iref) + \frac{1}{R}\frac{dVbe}{dT}
\frac{dIref}{dT} = (1060 ppm/deg C)(100uA) + \frac{1}{43K}(-2mV/deg C)
\frac{dIref}{dT} = 0.000000059 A/(deg C)
I think...
I have a simple current mirror made of BJTs and the output current needs to be 100uA and I am trying to balance a resistors positive temperature coefficient (1060 ppm) with the negative temperature coefficient of the BJTs to temperature compensate it. I am sure that the fractional temperature...
I am not sure if this is the right place to ask this. I am wondering how to convert to ppm/(deg C). I have a temperature coefficient I found and I am trying to convert the number to ppm/(deg C). The number I have is 0.000000059 A/(deg C) so do I just multiply it by 10^6 which gives me 0.059...
Homework Statement
NASA would like to place a satellite in orbit around the moon such that the satellite always remains in the same position over the lunar surface. What is the satellite's altitude?
Homework Equations
T^{2} = \left(\frac{4\pi^{2}}{GM}\right)r^{3}
The Attempt at a...
Ok I attempted this and here is what I got:
KVL:
iR + v = 0
iR + L\frac{di}{dt} = 0
\frac{di}{dt} = -\frac{iR}{L}
-\frac{di}{i} = \frac{R}{L}dt
-lni + C = \frac{R}{L}t
I_{L}(0)=1 A
-ln1 + C = \frac{R}{L}0
C = 0
-lni + 0 = \frac{R}{L}t
0 = \frac{R}{L}t + lni
1...
Homework Statement
The switch has been closed for a long time.
a) Current flowing through inductor. Voltage across it. IS any current flowing through the resistor.
b) The switch opens at t = 0s. Find an equation for the inductor voltage as a function of time for t > 0. How long does it take...
I used this formula:
v_{n} = v_{n-1} + a_{n}(0.1)
which is what you said but would the position be:
x_{n} = x_{n-1} + v_{n-1}(0.1) + (0.5)a_{n}(0.1)^{2}
y_{n} = y_{n-1} + v_{n-1}(0.1) + (0.5)a_{n}(0.1)^{2}
for every point?
Homework Statement
I have some data from a lab conducted with a accelerometer to collect the acceleration and I am trying to figure out how to create a v vs t graph from the a vs t graph. When I create the a vs t graph in excel its very crazy looking because of the change in acceleration at...
Homework Statement
Verify that the given functions form a fundamental set of solutions of the differential equation on the indicated interval. Form the solution.
4y^{''} - 4y^{'} + y = 0
e^{x/2}, xe^{x/2}
Homework Equations...
Homework Statement
Find an interval centered about x = 0 for which the given initial-value problem has a unique solution.
y^{''} + (tanx)y = e^{x}
y(0) = 1 y^{'}(0) = 0
Homework Equations
a_{i}(x), i=0,1,2,3,...,n is continuous and
a_{n} \neq 0 for every x in I.
The Attempt at a Solution...