Question

A multiloop circuit is given. It is not necessary to solve the entire circuit. In the figure shown, the current I2 is closest to

Answer 1

Concepts and reason

The concept used in this problem is Kirchhoff’s Current Law.

First, explain the Kirchhoff’s Current Law by using the circuit diagram. Later on, determine the value of current ${I_2}$ in the given circuit by using the concept of Kirchhoff’s Current Law.

Fundamentals

Kirchhoff’s Current Law:

This law states that the sum of incoming current to the junction is equal to the sum of outgoing current away from the junction.

The expression for the KCL is given by,

$\sum {{I_{{\rm{incoming}}}} = \sum {{I_{{\rm{outgoing}}}}} }$

Here, ${I_{{\rm{incoming}}}}$ is the incoming current t the junction and $\sum {{I_{{\rm{outgoing}}}}}$ is the outgoing current away from the junction.

The below figure shows the KCL at a junction.

Here, ${{\rm{I}}_{\rm{1}}}{\rm{ and }}{{\rm{I}}_{\rm{2}}}$ are incoming currents and ${{\rm{I}}_3}{\rm{, }}{{\rm{I}}_4}{\rm{ and }}{{\rm{I}}_{{\rm{5 }}}}$ are outgoing currents.

The expression for the KCL for the above figure is given by,

$\begin{array}{l}\\{I_1} + {I_2} = {I_3} + {I_4} + {I_5}\\\\{\rm{or}}\\\\{I_1} + {I_2} - {I_3} - {I_4} - {I_5} = 0\\\end{array}$

The below circuit follows the KCL to determine the current ${I_2}$ .

Refer to the above figure; at a node “e” $5{\rm{ A}}$ is going to the junction and ${\rm{3 A and }}{{\rm{I}}_2}$ is leaving the junction.

Apply KCL at node e and write the expression for current at node e.

$5{\rm{ A}} = {I_2} + 3{\rm{ A}}$

Solve the above equation for current ${I_2}$ .

$\begin{array}{c}\\{I_2} = 5{\rm{ A}} - 3{\rm{ A}}\\\\ = 2{\rm{ A}}\\\end{array}$

Ans:

The value of the current ${{\bf{I}}_{\bf{2}}}$ is ${\bf{2 A}}$ .