Calculate the total resistance of the circuit.

Steps to Solve

1. Identify the components of the circuit

The circuit consists of a 40V voltage source and several resistors: 5Ω, 10Ω, 8Ω, 18Ω, and 25Ω.

2. Group the resistors

The resistors are connected as follows:

• The 10Ω and 5Ω are in series.
• The 18Ω and 25Ω resistors are in parallel.

3. Calculate the equivalent resistance of the series resistors

For resistors in series, the total resistance ($R_{total, series}$) is calculated as:

$$ R_{total, series} = R_1 + R_2 $$

Here, $R_1 = 10Ω$ and $R_2 = 5Ω$:

$$ R_{total, series} = 10 + 5 = 15Ω $$

4. Calculate the equivalent resistance of the parallel resistors

For resistors in parallel, the total resistance ($R_{total, parallel}$) is calculated using the formula:

$$ \frac{1}{R_{total, parallel}} = \frac{1}{R_3} + \frac{1}{R_4} $$

Here, $R_3 = 18Ω$ and $R_4 = 25Ω$:

$$ \frac{1}{R_{total, parallel}} = \frac{1}{18} + \frac{1}{25} $$

Calculating this gives:

$$ \frac{1}{R_{total, parallel}} = \frac{25 + 18}{450} = \frac{43}{450} $$

Therefore:

$$ R_{total, parallel} = \frac{450}{43} \approx 10.47Ω $$

5. Combine the equivalent resistances

Now, we can find the total resistance ($R_{total}$) of the entire circuit by adding the series and parallel resistances:

$$ R_{total} = R_{total, series} + R_{total, parallel} $$

Substituting the values we calculated:

$$ R_{total} = 15 + 10.47 \approx 25.47Ω $$