A circuit with multiple sources of voltage

[ChessEnthusiast]

Homework Statement

Solve this circuit:
a) Mark all currents
b) Write a system of equations allowing you to solve for the currents2. The attempt at a solution
Part a) in attachment.
Part b)
$$\epsilon_1 = i_1 r_1 + (i_1 + i_2 + i_3) R$$
$$\epsilon_2 = i_2 r_2 + (i_1 + i_2 + i_3) R$$
$$\epsilon_3 = i_3 r_3 + (i_1 + i_2 + i_3) R$$

Is this solution valid?

 

[haruspex]

Homework Statement

Solve this circuit:
a) Mark all currents
b) Write a system of equations allowing you to solve for the currents2. The attempt at a solution
Part a) in attachment.
Part b)
$$\epsilon_1 = i_1 r_1 + (i_1 + i_2 + i_3) R$$
$$\epsilon_2 = i_2 r_2 + (i_1 + i_2 + i_3) R$$
$$\epsilon_3 = i_3 r_3 + (i_1 + i_2 + i_3) R$$

Is this solution valid?

Looks right.

 

[gneill]

That will work. Your equations look fine.