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Current Electricity

Question
CBSEENPH12040084

In the circuit shown, if a conducting wire is connected between points A and B, the current in this wire will



  • flow from A to B

  • flow in the direction which will be decided by the value of V

  • be zero

  • flow from B to A

Solution

D.

flow from B to A

Current will flow from higher to lower potential.
Resistances 4 space straight capital omega space and space 4 space straight capital omega are connected in series, so their effective resistance is                  straight R apostrophe space equals space 4 plus 4 space equals space 8 straight capital omega
  Similarly, 1 straight capital omega and 3 straight capital omega are in series
So,       straight R apostrophe apostrophe space equals space 1 plus 3 space equals space 4 straight capital omega
Now R' and R" will be in parallel, hence effective resistance
                          straight R space equals space fraction numerator straight R apostrophe space cross times space straight R " over denominator straight R apostrophe plus straight R apostrophe apostrophe end fraction
space space space space equals fraction numerator 8 cross times 4 over denominator 8 plus 4 end fraction space equals space 32 over 12 equals 8 over 3 straight capital omega
Current through the circuit, from Ohm's law
                         straight i space equals space straight V over straight R equals space fraction numerator 3 straight V over denominator 8 end fraction straight A
Let current straight i subscript 1 space and space straight i subscript 2 flow in the branches as shown:
therefore space space space space 8 straight i subscript 1 space equals space 4 straight i subscript 2
rightwards double arrow space space space space space straight i subscript 2 space equals space 2 straight i subscript 1
Also comma space space space space straight i space equals space straight i subscript 1 space plus space straight i subscript 2 space space space space space space space space space space space space space space space space space space space space... left parenthesis straight i right parenthesis
rightwards double arrow space space space space space space fraction numerator 3 straight V over denominator 8 end fraction space equals straight i subscript 1 plus 2 straight i subscript 1
rightwards double arrow space space space straight i subscript 1 space equals space straight V over 8 straight A
and space space straight i subscript 2 space equals space straight V over 4 straight A
 Potential space drop space at space straight A comma space straight V subscript straight A space equals space 4 space cross times space straight i subscript 1 space equals space fraction numerator 4 straight V over denominator 8 end fraction space equals space straight V over 2
Potential space drop space at space straight B comma space straight V subscript straight B space equals space 1 space cross times space straight i subscript 2 space equals space 1 cross times straight V over 4 space equals space straight V over 4
Since, drop of potential is greater in 4 straight capital omega resistance so. It will be at lower potential than B, hence, on connecting wire between points A and B, the current will flow from B to A.

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