You have three identical ohmic resistors, and all of the following statements ar

Question

You have three identical ohmic resistors, and all of the following statements are true: - Each resistor is a (right) cylinder of material with a mass of 0.0559 g. And each resistor just fits into its own individual rectangular packaging box, which has inner dimensions of 1.00 times 1.00 times 31.416 (lengths in mm). - If the three resistors are connected to a certain constant-voltage ideal batter)' (i.e. it has no internal resistance) the minimum possible total current would be 1.50 A. - If the three resistors are connected in a different configuration to that same constant-voltage battery, the total power produced will be 42.525 W. Estimate the mean time between collisions for electrons flowing in these resistors.

Explanation / Answer

we know that the current density J=I/A but considering electron density J=neV

where V is the drift velocity of the electron

again V=(eT/m)*E

from the given values m=m1+m2+m3= 3*.0559g=.16677g

I=1.50A

and P=42.525W

now n=free electron density=avogardo number*density/mass=avogardo number*M/V*1/M=avogardo number/V

=6.02*10^23/3*(.1*.1*3.1416)

again P=I.Voltage

or Voltage =P/I=42.525/1.50=28.35V

then R=P/I^2=18.9ohm

again we know that J=V/RM =28.35/18.9*.16677g

which is equal to n*e*v= 6.02*10^23/6.02*10^23/3*(.1*.1*3.1416). 1.6*10^-19*v

6.02*10^23/3*(.1*.1*3.1416). 1.6*10^-19.v=28.35/18.9*.16677

or drift velocity v=(28.35/18.9*.16677)(3*(.1*.1*3.1416)/6.02*10^23)*(1/1.6*10^-19)cm/s

or v=.088*10-4cm/s

then using

V=(eT/m)*E we get the T

but E=resistivity/current density=18.9/28.35/18.9*.16677=2.10

then T=V.m/e.E=.088*10-4*.16677/1.6*10^-19*2.10s=.0043*10^15s

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