(Solved): Consider the circuit in the figure, with the current directions defined as shown. There are fou ...

Consider the circuit in the figure, with the current directions defined as shown. There are four resistors in this circuit $$(R_1,R_2,R_3$$, and $$R_4)$$ and four batteries with emfs $${\mathcal{E}}_1=18\mathrm{V},{\mathcal{E}}_2$$ $$=5.5\mathrm{V},{\mathcal{E}}_3=9.5\mathrm{V}$$, and $${\mathcal{E}}_4=27\mathrm{V}$$, each with internal resistance given by $$r_1$$ as marked in the figure. Randomized Variables $$\begin{array}{l}{\mathcal{E}}_1=18\mathrm{V}\\ {\mathcal{E}}_2=5.5\mathrm{V}\\ {\mathcal{E}}_3=9.5\mathrm{V}\\ {\mathcal{E}}_4=27\mathrm{V}\end{array}$$ (a) Calculate the current $$I_1$$ in amps. (b) Calculate the current $$I_2$$ in amps. (c) Calculate the current $$I_3$$ in amps.