P1 Ps B3 Po Ps Three Identlcal light bulbs are connected to two batterles as sho

Question

P1 Ps B3 Po Ps Three Identlcal light bulbs are connected to two batterles as shown In the dlagram above To start the analysls of this clrcult you must wrlte energy conservatlon (loop) equatlons. Each equatlon must Involve a round-trip path that beglns and ends at the same location. Each segment of the path should go through a wire, a bulb, or a battery (not through the alr). How many valld energy conservation (loop) equatlons Is It posslble to wrlte for thls clrcult? -Select which of the following equations are valid energy conservation loop equations for thls circuit? El refers to the electric field In bulb #1, L refers to the length of a bulb filament, etc. Assume that the electric fleld In the connecting wires Is small enough to neglect.

Explanation / Answer

We can write 3 valid energy conservation ( loop ) equations.

valid energy conservation ( loop ) equations are

+2*emf - E1L - E3L = 0

+2*emf - E1L - E2L = 0

+E2L - E3L = 0

valid charge conservation equation for this circuit is i1 = i2 + i3

using the above equations

E2L = E3L

since current i = neAVd

n = density of charge carriers

A area of cross-section

Vd drift speed

and Vd = mE

m = mobility

E = Electric field

i =  neAVd = neAmE

since E2L = E3L and E2 = E3

i2 = i3

and since i1 = i2 +i3

neAmE1 = neAmE2 + neAmE3

and E1 = E2 + E3 = 2E2 = 2E3

hence +2*emf = E1L + E2L = 3E2L

E3 = 71.11 V/m

magnitude of electric field inside bulb#1, E1 = 142.22 V/m

magnitude of electric field inside bulb#2, E2 = 71.11 V/m

number of electrons that enter bulb#1 per second = nAmE1 = 1.21 x 1018 /s

number of electrons that enter bulb#2 per second = nAmE2 = 6.03 x 1017 /s

Please rate my answer if you find it helpful, good luck...

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