This circuit problem asks you to:

i) Use the current divider to find the current $I_1$. ii) Find the voltage $V_8$ across the 8Ω resistor. iii) Use the series and parallel equivalent circuit to find the power at the 10Ω resistor.

Let's go step by step for each part:

Step 1: Current Divider to Find $I_1$

The current divider rule helps us calculate the current through a particular branch when resistors are in parallel. From the given circuit, you need to find the current $I_1$ through the 8Ω resistor, knowing the total current is 15A.

The current divider formula is: $I_1 = I_{total} \times \frac{R_{total}}{R_1}$ Where:

• $I_{total}$ is the total current entering the parallel network (15A).
• $R_{total}$ is the equivalent resistance of the parallel combination of resistors in the branch.
• $R_1$ is the resistor through which you are calculating the current (in this case, the 8Ω resistor).

We need to first calculate the total parallel resistance of the network and then apply the formula.

Step 2: Finding Voltage $V_8$

To find the voltage across the 8Ω resistor ($V_8$), use Ohm's law: $V = I \times R$ You would calculate the current flowing through the 8Ω resistor and use that to find the voltage.

Step 3: Series and Parallel Equivalent Circuit to Find Power at the 10Ω Resistor

For power calculation, we use the formula: $P = \frac{V^2}{R}$ Where $V$ is the voltage across the 10Ω resistor, and $R$ is the resistance (10Ω).

We need to find the voltage across the 10Ω resistor and then use the power formula.

If you would like, I can guide you through these calculations step-by-step for more clarity.

Would you like to proceed with the detailed solutions for each part? Let me know if you need help with any specific section!