1.) How much would you have to raise the temperature of a copper wire (originall
ID: 2273349 • Letter: 1
Question
1.) How much would you have to raise the temperature of a copper wire (originally at 20?C) to increase its resistance by 18% ?
2.)
A.) Estimate how much energy is required to transmit one action potential along the axon 10
cm long of radius 30?m . The thickness of the membrane is about 10?8and the dielectric constant is about 3. [Hint: the energy to transmit one pulse is equivalent to the energy stored by charging the axon capacitance]. ANSWER IN J
B.) What minimum average power is required for
104 neurons each transmitting 150 pulses per second?
3.) A 3.6-
k?and a 2.3-k?resistor are connected in parallel; this combination is connected in series with a 1.5-k?resistor.
If each resistor is rated at 0.50W (maximum without overheating), what is the maximum voltage that can be applied across the whole network?
Explanation / Answer
The resistance of most materials (including copper) increases when the temperature rises.
The formula: R = R(o)[1 + alpha*delta T]
. In your question: if the resistance increases 19%,
then R = 1.18R(o)
=> 1.18R(o) = R(o) [ 1 + alpha*delta T].
We can cancel both sides by R(o) and we have: 1.18 = 1 + alpha*delta T)
Alpha is the thermal coefficient of resistivity for copper (4.29x10^-3)
=> 1.18 = 1 + (4.29x10^-3)(delta T)
=> 0.18 = (4.29x10^-3)(delta T)
=> delta T = (0.18)/(4.29x10^-3) = 44.3
Final temperature = 41.86degree C
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