Animated Solution for Physics - Current Electricity: In the given circuit diagram, the currents $I_1=-0.3$ A, $I_4=0.8$ A and $I_5=0.4$ A, are flowing as shown. The currents $I_2,I_3$ and $I_6$ respectively, are

Welcome to this interesting circuit bridge problem! We are given a network of resistors with several known currents flowing through them. Our mission is to find the missing currents: $I_2$, $I_3$, and $I_6$.

To solve this, we will rely on a fundamental principle of physics: Kirchhoff's Current Law (KCL).

KCL is simply the law of conservation of charge applied to a circuit. It states that at any junction (or node), the total current entering must be exactly equal to the total current leaving. No charge can magically appear or disappear at a node.

Let's start with the simplest junction in our circuit, node $P$. Look closely at the diagram.

The current $I_5$ is entering node $P$ from the bottom, and $I_6$ is leaving it to the right. There are absolutely no other paths connected to this node!

Therefore, the current entering must equal the current leaving:

Since we are given that $I_5=0.4\text{ A}$, it immediately follows that:

Now, let's move down to junction $S$ at the bottom left.

Here, the current $I_4$ is entering the node from the left side. Where does this current go? It splits into two paths: $I_5$ going upwards, and $I_3$ going diagonally towards the top right.

Applying KCL, the total entering current equals the sum of the leaving currents:

We can now substitute the known values into our equation:

Solving for $I_3$, we get:

Finally, let's tackle junction $Q$ at the top right. This node is a bit busier!

Currents $I_6$ and $I_3$ are both entering node $Q$. On the other hand, currents $I_1$ and $I_2$ are leaving it.

Setting the total entering current equal to the total leaving current gives us:

We substitute the values we know. Watch out for the minus sign on $I_1$!

Solving this, we find:

We have successfully found all the missing currents!

The calculated values are $I_2=1.1\text{ A}$, $I_3=0.4\text{ A}$, and $I_6=0.4\text{ A}$. This matches perfectly with option (a).

This problem was a great exercise in applying KCL systematically. Always trust the math, even if a current is negative. A negative current just means the physical flow of positive charge is opposite to the arrow drawn in the diagram. Keep practicing, and these node equations will become second nature to you!