This one has 3 loops. I need to assign a direction (e.g clockwise), form 3 equations and solve simultaneously. But I can't seem to do this question.
There's no voltage source on the third loop. Any help?
Mesh analysis with 3 loops
circuit analysis
Related Solutions
The equation for clockwise should be:
$$-v_{s} + (i_1 + i_s)R_2 + i_1R_3 = 0$$ $$-v_s + i_1(R_2+R_3) + i_sR_2 = 0$$ $$i_1 = - \frac{ i_sR_2 - v_s}{R_2+R_3}$$
Which is exactly negative of the other direction choice.
What I would do is completely ignore any of the voltage arrows for your analysis. You should be labeling the nodes and have a reference node anyways, which isn't present in that diagram.
For example, here I've removed those arrows, renamed nodes with lowercase letters, and designated a ground node at the bottom. Do all your analysis using Va, Vb, Vc, Vc, Vd, and Ve. Branch currents are assumed to follow the direction of the arrow on the branch (I1, I2, I3, I4, and I5).
edit:
Apparently, arrows denote the assumed positive potential as being from arrowhead minus arrowtail, so we can find that:
\begin{align} V_1 = V_b\\ V_2 = V_c \end{align}
Related Topic
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Best Answer
First hint refer to diagram below, can you find the voltage drop across R3. If the values of all R and V is given.
Edit : Second hint refer to your original diagram, (I3 - I1)(30) + I3(20) + (I3 - I2)(40) = 0. Refer to diagram below for the direction of the current assumed. Try browsing through this link for better understandings.
Example:
Refer to the picture below if you should get the correct equation by following the steps in the image Image Source
I feel that you are asking a fundamental question in electrical engineering, that's only reason for me not to give you a direct answer or solution instead I'll try my best to guide you to get the solution.