81. mmh Find the magnitude and the direction of the current in the 2.0 Ω resistor in the drawing.

Adding currents and reference points result in the new drawing.

We have three currents labeled, so we need three equations. First do a junction rule at point C

Need two loop rules, first use upper loop, go clockwise from point A and for the second rule use lower loop, go clockwise from point E.

Take the current junction and solve for i₁

Now plug that into the first loop equation

Consider the second loop equation

We will multiple the first loop equation by 3 and then add the two loop equations to solve for i₂.

Solve for i₂

Now since we find a positive value the assumed direction of i₂ is correct.

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This page last updated on June 18, 2018