We need three equations—Kirchhoff's loop rule:

$\overline{){\mathbf{\sum}}{\mathit{V}}{\mathbf{=}}{\mathbf{0}}}$ around each loop

Kirchhoff's junction rule:

$\overline{){\mathbf{\sum}}{{\mathit{i}}}_{\mathit{i}\mathit{n}}{\mathbf{=}}{\mathbf{\sum}}{{\mathit{i}}}_{\mathit{o}\mathit{u}\mathit{t}}}$ at each junction

and Ohm's Law

$\overline{){\mathit{V}}{\mathbf{=}}{\mathit{i}}{\mathit{R}}}$

We don't know *i*_{3}, but we know the other two currents, all the resistances, and one of three EMFs/voltages. Three unknowns: we need three equations.

(a) Find the emf *ε*_{1} in the circuit of the figure (Figure 1) .

(b) Find the emf *ε*_{2} in the circuit of the figure.

(c) Find the potential difference of point *b* relative to point *a*

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