How many arbitrary currents are needed to solve for the currents in a circuit?

[mmg0789]

Homework Statement

I just had a general question for solving for an unknown current(s) in single or multi-loops circuits. How exactly do we know how many arbitrary currents we need to define for solving the for the currents in the circuit? do we define a current for each loop that is present? for each voltage source? this always confuses me when I'm solving problems like these. any help is appreciated.

thanks

 

[Doc Al]

You won't go wrong if you first assign each branch its own current. Those currents are not all independent, as they are related by Kirchhoff's law.

 

[wimma]

You won't go wrong if you first assign each branch its own current. Those currents are not all independent, as they are related by Kirchhoff's law.

Al is right. Concentrate not on how many currents you worry about, but rather the fact that every circuit analysis problem you get is based on:
(a) V=IR for various components
(b) Kirchoff 1: the total voltage is equal to the sum of the voltages of each component in sequence. (V_T = V_1 + V_2 + ... + V_n)
(c) Kirchoff 2: the total current entering a junction is precisely equal to the total current exiting a junction. (I_in =I_out)

Then brace for epic win on your next circuits problem:grin:

 

[turin]

Or maybe (a) V=IZ, depending on your level.