The problem involves a circuit with eight identical resistors, each of resistance $R = 24 \, \Omega$, arranged in a particular configuration. The circuit is connected to a voltage source of 120 V, and the internal resistance is negligible. We are asked to determine the total current through the circuit.

Steps to solve:

1. Identify the Configuration: From the diagram, it appears that the resistors are arranged in two parallel groups, each consisting of four resistors in series.

2. Calculate the Equivalent Resistance for Each Series Group:

   • Each series group contains four resistors, so the total resistance for one series group is: $R_{\text{series}} = R + R + R + R = 4R = 4 \times 24 \, \Omega = 96 \, \Omega$

3. Calculate the Total Resistance:

   • The two groups are connected in parallel. The equivalent resistance of two resistances in parallel $R_{\text{parallel}}$ is given by: $\frac{1}{R_{\text{total}}} = \frac{1}{R_{\text{group1}}} + \frac{1}{R_{\text{group2}}} = \frac{1}{96 \, \Omega} + \frac{1}{96 \, \Omega}$ Simplifying: $\frac{1}{R_{\text{total}}} = \frac{2}{96} = \frac{1}{48}$ Therefore: $R_{\text{total}} = 48 \, \Omega$

4. Calculate the Current Using Ohm's Law:

   • From Ohm's law, $V = IR$, we can solve for the current $I$: $I = \frac{V}{R_{\text{total}}} = \frac{120 \, \text{V}}{48 \, \Omega} = 2.5 \, \text{A}$

Conclusion:

The current flowing through the circuit is $2.5 \, \text{A}$.

Would you like any further details or have any questions?

Here are 5 related questions to expand on this topic:

1. How would the total resistance change if the resistors were arranged in series instead of parallel?
2. What happens to the current if the voltage is doubled but the resistance remains the same?
3. How does the power dissipated by each resistor relate to the total current in the circuit?
4. What is the effect on the total current if an additional parallel branch is added with four more resistors?
5. How would the current change if each resistor had a resistance of $12 \, \Omega$ instead of $24 \, \Omega$?

Tip: Always remember that resistors in series add directly, while resistors in parallel follow the reciprocal addition rule!