1. **State the problem:** Two resistors of 8 ohms and 10 ohms are connected in parallel, and the total current flowing through the combination is 9 A. We need to find the current flowing through the 8-ohm resistor. 2. **Formula and rules:** In a parallel circuit, the voltage across each resistor is the same. The total current $I_{total}$ is the sum of the currents through each resistor: $$I_{total} = I_1 + I_2$$ Ohm's law relates current, voltage, and resistance: $$I = \frac{V}{R}$$ Since voltage $V$ is the same across both resistors, we can express currents as $$I_1 = \frac{V}{R_1}$$ and $$I_2 = \frac{V}{R_2}$$. 3. **Find the voltage across the resistors:** Using total current and equivalent resistance. The equivalent resistance $R_{eq}$ for resistors in parallel is given by: $$\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} = \frac{1}{8} + \frac{1}{10} = \frac{5}{40} + \frac{4}{40} = \frac{9}{40}$$ So, $$R_{eq} = \frac{40}{9} \approx 4.44\, \Omega$$ 4. **Calculate voltage $V$ using total current:** $$V = I_{total} \times R_{eq} = 9 \times \frac{40}{9} = 40\, \text{volts}$$ 5. **Calculate current through 8-ohm resistor:** $$I_1 = \frac{V}{R_1} = \frac{40}{8} = 5\, \text{A}$$ **Final answer:** The current flowing through the 8-ohm resistor is **5 A**.