Two Nichrome wires The following questions refer to the circuit shown in the fig

Question

Two Nichrome wires The following questions refer to the circuit shown in the figure, consisting of two flashlight batteries and two Nichrome wires of different lengths and different thicknesses as shown (corresponding roughly to your own thick and thin Nichrome wires). The thin wire is 51 cm long, and its diameter is 0.25 mm. The thick wire is 15 cm long, and its diameter is 0.38 mm.

(a) The emf of each flashlight battery is 1.5 volts. Determine the steady-state electric field inside each Nichrome wire. Remember that in the steady state you must satisfy both the current node rule and energy conservation. These two principles give you two equations for the two unknown fields.

E inside thin wire = V/m

E inside thick wire = V/m

(b) The electron mobility in room-temperature Nichrome is about 7 10-5 (m/s)/(N/C). How long (in minutes) does it take an electron to drift through the two Nichrome wires from location B to location A? min

(c) On the other hand, about how long did it take to establish the steady state when the circuit was first assembled? Give an approximate, not precise numerical answer. s

(d) There are about 9 1028 mobile electrons per cubic meter in Nichrome. How many electrons cross the junction between the two wires every second? electrons/s

Explanation / Answer

R = L/A for the resistance of a wire with length L, constant resistivity and constant cross-section area A to get the resistances R1, R2 of the wire segments. Then I = Vtotal/Rtotal = 3V/(R1+R2). In the segments you have V1 = I*R1, V2 = I*R2; and from these you have E1 and E2

=1.1e-6

R1= 1.1e-6* 0.51/0.049e-6 =11.45 ohm

R2 = 1.1e-6* 0.15/0.11335e-6= 1.456 ohm

I= 3V/12.906= 0.2324 V
------------------
Vdthin=U*Ethin
Vdthick=U*Ethick

Time taken for:
Thin: t_thin=L_thin/Vdthin
Thick: t_thick= L_thick/ Vdthick
B to A: t= t_thin + t_thick = time in sec (should end up being 2000sec +/- a couple hundred)
then just divide by 60sec/min.

c) time=L/c
L=Length of thin+ Length of thick =0.51+0.15 =0.66 m
c=3e8 m/s = speed of light

t= 0.66*3e8=1.98e8 s

d) i = nAuE = nA*Vdrift
where n=9e28 e-/sec and A=cross-sect. area
and assuming i_thin=i_thick

Therefore,electrons cross the junction between the two wires every second = 9e28 e-/sec

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