*84. Determine the voltage across the 5.0 Ω resistor in the drawing. Which end of the resistor is at the higher potential?

Figure below provides currents and reference points for writing out a set of Kirckhoff laws.

Do a junction rule at point B

Need two loop rules, do one on left start on point A and go clockwise, for the second do right loop start at point B and again go clockwise.

Need to solve for i₁ in order to find voltage across the 5.0 Ω resistor. So the simplified set of equations presented below.

Use the relationship from the junction rule to substitute for i₂ in the two loop equations

Simplifying these two expressions

Multiply the first equation by 2 and then subtract the second equation from the first.

So the voltage across the 5.0 Ω is

Since the current found is positive, the assumed direction of i₁ is correct. Therefore the voltage would drop going to the right, which means the left side of the resistor is the higher voltage.

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This page last updated on June 18, 2018