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Q

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)

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

122 Views

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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