# Problem: A. In the circuit shown in the figure, find the magnitude of current in the upper branch.B. Find the magnitude of current in the middle branch.C. Find the magnitude of current in the lower branch.D. What is the potential difference Vab of point a relative to point b?

###### FREE Expert Solution

Kirchhoff's loop rule:

$\overline{){\mathbf{\Sigma }}{\mathbf{V}}{\mathbf{=}}{\mathbf{0}}}$

A. Considering the upper loop:

Applying Kirchhoff's loop rule in L1

$\begin{array}{rcl}\begin{array}{rc}{\mathbf{i}}_{\mathbf{1}}\mathbf{3}\mathbf{.}\mathbf{00}\mathbf{\Omega }& \mathbf{-}\mathbf{10}\mathbf{.}\mathbf{00}\mathbf{V}\mathbf{+}{\mathbf{i}}_{\mathbf{1}}\mathbf{2}\mathbf{.}\mathbf{00}\mathbf{\Omega }\mathbf{+}\mathbf{\left(}{\mathbf{i}}_{\mathbf{1}}\mathbf{-}{\mathbf{i}}_{\mathbf{2}}\mathbf{\right)}\mathbf{1}\mathbf{.}\mathbf{00}\mathbf{\Omega }\mathbf{+}\mathbf{5}\mathbf{.}\mathbf{00}\mathbf{V}\mathbf{-}\mathbf{\left(}{\mathbf{i}}_{\mathbf{2}}\mathbf{-}{\mathbf{i}}_{\mathbf{1}}\mathbf{\right)}\mathbf{4}\mathbf{.}\mathbf{00}\mathbf{\Omega }\end{array}& \mathbf{=}& \mathbf{0}\\ {\mathbf{i}}_{\mathbf{1}}\mathbf{5}\mathbf{.}\mathbf{00}\mathbf{\Omega }\mathbf{+}{\mathbf{i}}_{\mathbf{1}}\mathbf{1}\mathbf{.}\mathbf{00}\mathbf{\Omega }\mathbf{-}{\mathbf{i}}_{\mathbf{2}}\mathbf{1}\mathbf{.}\mathbf{00}\mathbf{\Omega }\mathbf{-}{\mathbf{i}}_{\mathbf{2}}\mathbf{4}\mathbf{.}\mathbf{00}\mathbf{\Omega }\mathbf{+}{\mathbf{i}}_{\mathbf{1}}\mathbf{4}\mathbf{.}\mathbf{00}\mathbf{\Omega }\mathbf{-}\mathbf{5}\mathbf{.}\mathbf{00}\mathbf{V}& \mathbf{=}& \mathbf{0}\\ {\mathbf{i}}_{\mathbf{1}}\mathbf{10}\mathbf{.}\mathbf{00}\mathbf{\Omega }\mathbf{-}{\mathbf{i}}_{\mathbf{2}}\mathbf{5}\mathbf{.}\mathbf{00}\mathbf{\Omega }\mathbf{-}\mathbf{5}\mathbf{.}\mathbf{00}\mathbf{V}& \mathbf{=}& \mathbf{0}\\ {\mathbf{i}}_{\mathbf{1}}\mathbf{10}\mathbf{.}\mathbf{00}\mathbf{\Omega }\mathbf{-}{\mathbf{i}}_{\mathbf{2}}\mathbf{5}\mathbf{.}\mathbf{00}\mathbf{\Omega }& \mathbf{=}& \mathbf{5}\mathbf{.}\mathbf{00}\mathbf{V}\end{array}$

###### Problem Details

A. In the circuit shown in the figure, find the magnitude of current in the upper branch.

B. Find the magnitude of current in the middle branch.

C. Find the magnitude of current in the lower branch.

D. What is the potential difference Vab of point a relative to point b?

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Kirchhoff's Loop Rule concept. You can view video lessons to learn Kirchhoff's Loop Rule. Or if you need more Kirchhoff's Loop Rule practice, you can also practice Kirchhoff's Loop Rule practice problems.