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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