The image you've uploaded depicts an electrical circuit involving resistors and a voltage source. The task is to determine:

1. The total resistance.
2. The current flowing through the circuit.
3. The resistance of the 0.8 Ω resistor.

Let's break it down:

Step 1: Analyzing the Circuit

From the image:

• We have a series-parallel combination of resistors.
• The resistances are:
  • 6 Ω
  • 2 Ω
  • 0.8 Ω
• A 12 V battery is connected to the circuit.

Step 2: Calculating Total Resistance (R_total)

The resistors 6 Ω and 2 Ω are in series, so their combined resistance (R1) is: $R1 = R_{\text{6Ω}} + R_{\text{2Ω}} = 6Ω + 2Ω = 8Ω$ Now, this combination (R1) is in parallel with the 0.8 Ω resistor. To calculate the total resistance (R_total), we use the parallel formula: $\frac{1}{R_{\text{total}}} = \frac{1}{R1} + \frac{1}{R_{\text{0.8Ω}}}$ Substitute the values: $\frac{1}{R_{\text{total}}} = \frac{1}{8} + \frac{1}{0.8}$

Now, calculate the total resistance (R_total).

Step 3: Calculating the Current

Once we find the total resistance (R_total), we can use Ohm’s law to find the current: $I = \frac{V}{R_{\text{total}}}$ where $V = 12V$.

I'll first calculate the total resistance and the current for you.

Let me compute that! Given values R_6 = 6 # Ohms R_2 = 2 # Ohms R_08 = 0.8 # Ohms V = 12 # Voltage in volts

Calculate the total resistance R1 for the resistors in series (6Ω and 2Ω)

R1 = R_6 + R_2

Calculate the total resistance in parallel with the 0.8Ω resistor

R_total_inv = (1 / R1) + (1 / R_08)

Find the total resistance

R_total = 1 / R_total_inv

Calculate the current using Ohm's law: I = V / R_total

I = V / R_total

R_total, IThe calculations yield the following results:

1. Total Resistance (R_total): $0.73 \, \Omega$
2. Current (I): $16.5 \, \text{A}$

If you have any more questions or need further explanations, feel free to ask!

Here are some related questions that might interest you:

1. How do you calculate the total resistance for resistors in series and parallel?
2. What is the effect of increasing the resistance in a parallel circuit?
3. How can you calculate the power dissipated in this circuit?
4. What would happen if the voltage across the circuit were to change?
5. How does Ohm’s Law apply to both series and parallel circuits?

Tip: In parallel circuits, the total resistance is always less than the smallest resistor in the circuit.