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

See the electrical circuit shown in this figure. Which of the following equations is a correct equation for it?
  1. $\varepsilon_1-\left(\mathbf{i}_1+\mathbf{i}_2\right) \mathrm{R}-\mathrm{i}_1 \mathbf{r}_1=0$
  2. $\varepsilon_2-i_2 \mathbf{r}_2-\varepsilon_1-i_1 \mathbf{r}_1=0$
  3. $-\varepsilon_2-\left(i_1+i_2\right) R+i_2 r_2=0$
  4. $\varepsilon_1-\left(\mathrm{i}_1+\mathrm{i}_2\right) \mathrm{R}+\mathrm{i}_1 \mathrm{r}_1=0$

Solution

Key Idea Apply Kirchhoff' second law also called loop rule. The algebraic sum of the changes in potential in complete transversal of a mesh (closed loop) is zero. $i e, \Sigma \mathrm{V}=0$ Here $\varepsilon_1-\left(i_1+i_2\right) R-i_1 r_1=0$ If there are $n$ meshes in a circuit, the number of independent equations in accordance with loop law will be $(n-1)$.

Asked in: NEET 2009 (Screening)

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