Step 1: Analyze the circuit and identify resistor combinations:
The given circuit includes the following resistors:
- Two 6 Ω resistors are connected in parallel.
- Two 3 Ω resistors are connected in series with the equivalent of the 6 Ω parallel combination.
Step 2: Calculate the equivalent resistance of the parallel resistors:
When two resistors \( R_1 \) and \( R_2 \) are in parallel, the combined resistance \( R_{\text{parallel}} \) is given by:
\[
\frac{1}{R_{\text{parallel}}} = \frac{1}{R_1} + \frac{1}{R_2}
\]
Substitute the values:
\[
\frac{1}{R_{\text{parallel}}} = \frac{1}{6} + \frac{1}{6} = \frac{2}{6} = \frac{1}{3}
\]
\[
R_{\text{parallel}} = 3\,\Omega
\]
So, the two 6 Ω resistors in parallel are equivalent to a single 3 Ω resistor.
Step 3: Add the resistors in series:
Now, we add the two 3 Ω resistors in series with the 3 Ω equivalent resistance we just found:
\[
R_{\text{total}} = 3\,\Omega + 3\,\Omega + 3\,\Omega = 9\,\Omega
\]
So, the total resistance of the circuit is 9 Ω.
Step 4: Apply Ohm’s Law to find the total current:
Ohm’s Law is given by:
\[
I = \frac{V}{R}
\]
Where:
- \( V = 4.5\,\text{V} \) (the total voltage from the source)
- \( R_{\text{total}} = 9\,\Omega \) (the total resistance in the circuit)
Substitute the values:
\[
I = \frac{4.5}{9} = 0.5\,\text{A}
\]
Step 5: Conclusion:
The total current flowing through the circuit is 0.5 A.