In the circuit shown below, the connecting wires are much thicker and have much
ID: 1649686 • Letter: I
Question
In the circuit shown below, the connecting wires are much thicker and have much higher mobility and electron density than the filaments in the light bulbs. The length of the filament in the "long" bulb (green, top branch) is the same as the "round" bulb (orange, lower branch). They are made of the same material, and therefore have the same electron density and mobilities.
i. If currents of i2 = 2.9 x 10^18 electrons per sec, i3 = 4.1 x 10^18 electrons per second are given, what is the electron current through i1 going through the green bulb?
For the next questions, provide an explanation to why you chose that answer.
ii. The magnitude of the potential difference across the green bulb is ________.
a) greater than the magnitude of the potential difference across the orange bulb
b) less than the magnitude of the potential difference across the orange bulb
c) equal to the magnitude of the potential difference across the orange bulb
d) not enough information
iii. The magnitude of the net electric field in the filament of the green bulb is ________.
a) greater than the magnitude of the electric field in the orange bulb filament
b) less than the magnitude of the electric field in the orange bulb filament
c) equal to the magnitude of the electric field in the orange bulb filament
d) not enough information
iv. The cross sectional area of the filament of the long bulb is _________.
a) greater than the cross sectional area of the orange bulb filament
b) lesthan the cross sectional area of the orange bulb filament
c) equal to the cross sectional area of the orange bulb filament
d) not enough information
4 2Explanation / Answer
1) By the Kirchoff's current law, i1+i2=i3
so i1=i3-i2, i1=(4.1-2.9)*1018electrons/sec = 1.2*1018 electrons/sec.
2) potential difference across the bulb is given by V= IR
Mobility of electrons in both filaments are are same hence both BULBS HAVE same resistance.
so current through orange bulb is more than green bulb .So magnitude of potential differnce across green bulb is less than the magnitude of potential difference across orange bulb. -(b)
3) electric field is directly proportional to the potential. so the magnitude of net electric field in the filament of green bulb is less than the magnitude of electric field in the orange bulb filament -(b)
(4) Resistance is given by R=rho*length/area. Both filaments have same resistance as both have same mobility of electrons. Both are of same materials and filament lenghta are same for both. So both filaments must have same cross sectional area. ----------------------------(c)