Inductor and bulb in an circuit

[aryan pandey]

Homework Statement

the problem statement is provided in the attached file

Homework Equations

logic based , basic principle of inductors.

The Attempt at a Solution

after switch is opened the more the current passes through the bulb , more will be the brightness .
earlier in the steady state , current through each bulb will be E/R ( assuming power supply of emf E and each bulb of resistance R).
after the switch is opened the inductor will oppose the change in current in its branch and hence same amount of current will flow as it was flowing the inductors earlier ,
so current in bulb B and C would remain same but in Bulb A current flow will be doubled (2E/R).
hence brightness of bulb A should increase and rest should remain same .

BUT in the answer it is given take brightness of bulb C should increase and rest should remain same.
WHAT is wrong in my approach?

 

[TSny]

For convenience, here's the rotated picture.

 

[aryan pandey]

oh yeah thank u

 

[TSny]

I agree with your answer and reasoning. The brightness of A increases while B and C do not change.

 

[aryan pandey]

but why is the answer saying it otherway around

 

[rude man]

EDIT: I agree with the OP and TSny.
(Current in A reverses & doubles.)

 

[TSny]

I replaced the switch with a variable resistor that has zero resistance at t = 0 but increases fairly rapidly after t = 0. I then used Mathematica to solve the differential equations for the currents. It gives the following graph for the currents as a function of time:
https://www.physicsforums.com/attachments/upload_2017-2-14_11-7-47-png.113214/
The blue curve is the current in bulb A, the orange curve is the current in bulb B, and the green one is bulb C. All currents are equal to 1.0 at t = 0.

The current in A rapidly reverses direction and momentarily becomes greater in magnitude than its initial value. The currents in B and C never become greater than their initial values.

When I tried to make the variable resistor increase more rapidly (to better mimic the switch), Mathematica had trouble solving the equations. But the result above does at least show the general behavior.

 

[aryan pandey]

that great thank you for the explanation .