Question

Three identical light bulbs are connected to two batteries as shown in the diagram above.

To start the analysis of this circuit you must write energy conservation (loop) equations. Each equation must involve around-trip path that begins and ends at the same location. Each segment of the path should go through a wire, a bulb, or a battery(not through the air). How many valid energy conservation (loop)equations is it possible to write for this circuit?---Select---012345

Which of the following equations are valid energy conservation(loop) equations for this circuit?E₁ refers to the electric field in bulb #1, L refers to the length of a bulb filament, etc. Assume that the electric field in the connecting wires is small enough to neglect.

• +2*emf -E₁L- E₂L = 0

• E₁L -E₂L = 0

• E₁L -E₃L = 0

• +2*emf -E₁L-E₂L - E₃L= 0

• +2*emf -E₂L- E₃L = 0

• +E₂L -E₃L = 0

• +2*emf -E₁L- E₃L = 0

• 
  
  It is alsonecessary to write charge conservation equations (node) equations.Each such equation must relate electron current flowing into anodeto electron current flowing out of a node. Which of the followingare valid charge conservation equations for this circuit?
  

• i₁=i₂

• i₁=i₃

• i₁ =i₂ + i₃

• 
  
  Each battery hasan emf of 1.3 volts. Thelength of thetungsten filament in each bulb is 0.015 m. The radius of the filament is 5e-6 m (itis very thin!). The electron mobility of tungsten is1.8e-3(m/s)/(V/m). Tungsten has 6e+28 mobile electrons per cubicmeter.
  
  Since there are three unknown quantities, we need three equationsrelating these quantities. Use any two valid energy conservationequations and one validcharge conservation equation to solve forthe following electric field magnitudes:
  What is the magnitude of the electric field inside bulb #1?
  E₁ =V/m
  What is the magnitude of the electric field inside bulb #2?
  E₂ =V/m
  How many electrons per second enter bulb #1?
  i₁ =electrons/s
  How many electrons per second enter bulb #2?
  i₂ =electrons/s

Answer 1

The following are the valid energy conservation equations for this circuit: and From equation (C): The charge conservation equation for this circuit is 1 23 The relation between the drift velocity and the current is, inqAV The drift velocity in terms of mobility is, From (2) From (1) 1 23

E E+E -2E2 2E, From (D) From (B): +2emf-EL-E,L = 0 2 +2em 2 3L 2(1.3 V) 3(0.01m) 86.67 V/m The magnitude of the electric field in bulb 2 is 86.67 V/m. The magnitude of the electric field in bulb 1 is, 2(86.67 V/m)

-173.34 V/m The number of electrons that enter bulb 1 per second are, Number of electrons in bulb 1 = nAmE1 v) 6x1028 electrons) π (5x10-6 m) 1.8×10-3 173.34 V/nm (V/m) = 1.46981018 electrons The number of electrons that enter bulb 2 per second are. Number of electrons in bulb 2 nAmE 6x1028 electrons (5x10-6 m1.8x103 86.67 V/m (V/m) 7.347 x10' electrons