Can u please find the values of current I1, I2, and I3 in the given figure... Answer is given in fig.

To determine the values of currents I1, I2, and I3 in the given circuit, we need to apply some fundamental principles of electrical circuits, particularly Ohm's Law and Kirchhoff's laws. Although I can't see the figure you're referring to, I can guide you through the general approach to solve such problems.

Understanding the Circuit

First, let's identify the components in the circuit. Typically, a circuit diagram will include resistors, voltage sources, and possibly other elements like capacitors or inductors. The currents I1, I2, and I3 will depend on how these components are arranged—whether in series or parallel—and their respective values.

Applying Kirchhoff's Laws

We can use Kirchhoff's Current Law (KCL) and Kirchhoff's Voltage Law (KVL) to analyze the circuit:

• KCL: The sum of currents entering a junction equals the sum of currents leaving that junction.
• KVL: The sum of the electrical potential differences (voltage) around any closed network is zero.

Steps to Solve for Currents

Here’s a structured approach to find the currents:

1. Identify Nodes: Look for junction points in the circuit where currents converge or diverge.
2. Write KCL Equations: For each node, write down the KCL equation. For example, if I1 enters a node and I2 and I3 leave, the equation would be I1 = I2 + I3.
3. Analyze Loops: Choose loops in the circuit and apply KVL. Write down equations based on the voltage drops across resistors (using Ohm's Law: V = IR) and the voltage sources.
4. Substitute and Solve: You will end up with a system of equations. Use substitution or matrix methods to solve for the unknown currents I1, I2, and I3.

Example Scenario

Imagine a simple circuit with a 12V battery connected to two resistors, R1 = 4Ω and R2 = 2Ω, in parallel, and a resistor R3 = 3Ω in series with the parallel combination. The currents can be calculated as follows:

• First, find the equivalent resistance of R1 and R2:

1/R_eq = 1/R1 + 1/R2 = 1/4 + 1/2 = 3/4 → R_eq = 4/3Ω

• Next, find the total resistance in the circuit:

R_total = R_eq + R3 = 4/3 + 3 = 13/3Ω

• Now, calculate the total current from the battery using Ohm's Law:

I_total = V/R_total = 12V / (13/3Ω) = 36/13 A

• Using KCL at the node where I_total splits into I1 and I2:

I_total = I1 + I2

• Then, calculate I1 and I2 using the voltage across the parallel resistors:

V_parallel = I_total * R_eq = (36/13) * (4/3) = 48/13 V

• Finally, apply Ohm's Law to find I1 and I2:

I1 = V_parallel / R1 = (48/13) / 4 = 12/13 A

I2 = V_parallel / R2 = (48/13) / 2 = 24/13 A

Final Thoughts

By following these steps, you can systematically find the values of I1, I2, and I3 in your circuit. If you have specific values or a particular configuration in your figure, feel free to share those details for a more tailored solution!