The circuit shown is a combination of series and parallel resistors. Let's break it down and calculate the total resistance step by step, followed by the current using Ohm's law.

Step-by-step solution:

1. Identify the structure:

   • The resistors are arranged in a combination of series and parallel connections.
   • In the middle, there are two 4-ohm resistors connected in parallel.

2. Calculate the equivalent resistance for the two 4-ohm resistors in parallel: For resistors $R_1$ and $R_2$ in parallel, the equivalent resistance $R_{eq}$ is given by: $\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2}$ Substituting $R_1 = 4 \, \Omega$ and $R_2 = 4 \, \Omega$: $\frac{1}{R_{eq}} = \frac{1}{4} + \frac{1}{4} = \frac{2}{4} = \frac{1}{2}$ So, the equivalent resistance of the parallel section is: $R_{eq} = 2 \, \Omega$

3. Simplify the circuit:

   • The two 4-ohm resistors are now replaced by a single 2-ohm resistor.
   • This 2-ohm resistor is in series with the 2-ohm resistor on the left, the 1-ohm resistor on the far left, and the 5-ohm resistor on the right.

4. Sum the resistances in series: In a series circuit, the total resistance is the sum of all the resistances. So the total resistance $R_{total}$ is: $R_{total} = 1 \, \Omega + 2 \, \Omega + 2 \, \Omega + 5 \, \Omega = 10 \, \Omega$

5. Find the current using Ohm's law: Ohm's law states: $I = \frac{V}{R}$ Here, $V = 15 \, \text{V}$ (the battery voltage), and $R = 10 \, \Omega$ (the total resistance). So the current is: $I = \frac{15}{10} = 1.5 \, \text{A}$

Final Answer:

The current flowing through the circuit is $1.5 \, \text{A}$.

Would you like any more details or clarifications?

Here are five related questions for further exploration:

1. How would the total resistance change if one of the 4-ohm resistors was removed?
2. What would happen to the current if the voltage of the battery was increased to 20 V?
3. If the resistors were all connected in parallel, how would the total resistance be calculated?
4. How does the equivalent resistance change if the 5-ohm resistor was doubled to 10 ohms?
5. What effect does adding another resistor in series have on the overall current in the circuit?

Tip: Always remember to simplify the circuit step-by-step by identifying parallel and series connections when calculating total resistance.