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Find the current using Kirchhoff's Current Law.

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Find the current which flows through each of the four resistors in the figure (please see attachment).

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See attached file.
At junction B, by KCL (Kirchhoff's current law):
sum(Ii) = 0 => I1+I2 - I3 = 0
=> I3 = I1 + I2 .... (1)

For closed loop ABEFA, by KVL (Kirchhoff's voltage law):
sum(Ii*Ri) = sum(Ei) (take clockwise as +ve direction):
I3*R4 + I1*R1 = E1 ..........(2)
For closed mesh or ...

Solution Summary

The current is found using Kirchhoff's current law. The flows through each of the four resistors in a figure are given.