This problem is about a parallel circuit where two resistors, $R_1$ and $R_2$, are connected in parallel, and the current $I_1 = 7 \, \text{A}$ is flowing through the branch containing $R_1$.

Given:

• $R_1 = 10 \, \Omega$
• $R_2 = 11 \, \Omega$
• $I_1 = 7 \, \text{A}$

To determine the current through $R_2$, we can use Ohm's law and the fact that the voltage across both resistors in parallel is the same.

Step 1: Calculate the voltage across $R_1$

Using Ohm's law: $V = I_1 \times R_1$ $V = 7 \, \text{A} \times 10 \, \Omega = 70 \, \text{V}$ Since the resistors are in parallel, the voltage across $R_2$ is also 70 V.

Step 2: Calculate the current through $R_2$

Using Ohm's law for $R_2$: $I_2 = \frac{V}{R_2}$ $I_2 = \frac{70 \, \text{V}}{11 \, \Omega} \approx 6.4 \, \text{A}$

Thus, the current flowing through $R_2$ is approximately $\boxed{6.4 \, \text{A}}$.

Would you like more details on how to approach such problems or have any questions? Here are some related questions you can explore:

1. How is the total current in the circuit calculated in a parallel circuit?
2. What happens to the current distribution if the resistances are unequal in a parallel circuit?
3. How does the total resistance of a parallel circuit compare to individual resistances?
4. What would happen to the currents if we change the value of one resistor?
5. How can we calculate the total power consumed in this circuit?

Tip: In a parallel circuit, the voltage across each branch is the same, while the current divides based on the resistances of each branch.