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Please,please help me See the electric circuit shown in the figure.Which of the following equations is a correct equation for it?

See the electric circuit shown in the figure.

Which of the following equations is a correct equation for it?

  • Option 1)

    \varepsilon _{2}-i_{2}\ r_{2}-\varepsilon _{1} -i_{1}\ r_{1}=0

  • Option 2)

    -\varepsilon _{2}-\left ( i_{1}+i_{2} \right )R+i_{2}\ r_{2}=0

  • Option 3)

    \varepsilon _{2}-\left ( i_{1}+i_{2} \right )R+i_{1}\ r_{1}=0

  • Option 4)

    \varepsilon _{1}-\left ( i_{1}+i_{2} \right )R-i_{1}\ r_{1}=0

 
Answers (1)
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In closed loop -

-i_{1}}R_{1} + i_{2}}R_{2} -E_{1}-i_{3}}R_{3}+E_{2}+E_{3}-i_{4}}R_{4}=0

- wherein

 

 Apply Kirchoff law:

+\xi _{1}-i_{2}r_{2}-\xi_{2}+i_{1}r_{1}=0\:\:\:\:\:\:\:\:\:\:\:-(I)

or, \:\xi _{1}-i_{1}r_{1}-(i_{1}+i_{2})R=0


Option 1)

\varepsilon _{2}-i_{2}\ r_{2}-\varepsilon _{1} -i_{1}\ r_{1}=0

This option is incorrect.

Option 2)

-\varepsilon _{2}-\left ( i_{1}+i_{2} \right )R+i_{2}\ r_{2}=0

This option is incorrect.

Option 3)

\varepsilon _{2}-\left ( i_{1}+i_{2} \right )R+i_{1}\ r_{1}=0

This option is incorrect.

Option 4)

\varepsilon _{1}-\left ( i_{1}+i_{2} \right )R-i_{1}\ r_{1}=0

This option is correct.

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