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Electric Charges And Fields

Question
CBSEENPH12040033

See the electrical circuit shown in this figure. Which of the following equations is a correct equation for it?

  • straight epsilon subscript 1 minus left parenthesis straight i subscript 1 plus straight i subscript 2 right parenthesis space straight R space minus straight i subscript 1 straight r subscript 1 space equals space 0
  • straight epsilon subscript 2 minus straight i subscript 2 straight r subscript 2 minus straight epsilon subscript 1 space minus space straight i subscript 1 straight r subscript 1 space equals 0
  • negative space straight epsilon subscript 2 space minus left parenthesis straight i subscript 1 space plus straight i subscript 2 right parenthesis space straight R space plus space straight i subscript 1 straight r subscript 2 space equals space 0
  • straight epsilon subscript 1 space minus space left parenthesis straight i subscript 1 space plus straight i subscript 2 right parenthesis straight R space plus straight i subscript 2 straight r subscript 1 space equals space 0

Solution

A.

straight epsilon subscript 1 minus left parenthesis straight i subscript 1 plus straight i subscript 2 right parenthesis space straight R space minus straight i subscript 1 straight r subscript 1 space equals space 0

Apply Kirchhoff;s second law also called loop rule.
The algebraic sum of the changes in potential in complete transversal fo a mesh (closed loop) is zero ie , 
Here, straight epsilon subscript 1 minus left parenthesis straight i subscript 1 space plus space straight i subscript 2 right parenthesis space straight R space minus space straight i subscript 1 straight r subscript 1 space equals 0