The last kind of circuit is a combination circuit. A combination circuit has light bulbs arranged in both series and parallel. In one combination circuit, for example, current might travel through one branch where two components are arranged in series, and then travel through another branch with multiple components arranged in parallel.

It seems like you're describing a combination circuit, which is a type of electrical circuit that includes both series and parallel components. Let's break down the key concepts and characteristics of combination circuits step by step. ### Key Concepts 1. **Series Circuit**: - In a series circuit, components are connected end-to-end, so the same current flows through all components. - The total resistance in a series circuit is the sum of the individual resistances: \[ R_{total} = R_1 + R_2 + R_3 + \ldots \] 2. **Parallel Circuit**: - In a parallel circuit, components are connected across the same voltage source, so the voltage across each component is the same. - The total resistance in a parallel circuit can be calculated using the formula: \[ \frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \ldots \] 3. **Combination Circuit**: - A combination circuit contains both series and parallel components. - To analyze a combination circuit, you typically simplify it step by step: - First, calculate the equivalent resistance of the series components. - Then, calculate the equivalent resistance of the parallel components. - Finally, combine these results to find the total resistance of the circuit. ### Example Analysis Let's consider a simple example of a combination circuit: - **Components**: - Two resistors \( R_1 = 4 \, \Omega \) and \( R_2 = 6 \, \Omega \) in series. - A third resistor \( R_3 = 3 \, \Omega \) in parallel with the series combination of \( R_1 \) and \( R_2 \). ### Step-by-Step Solution 1. **Calculate the equivalent resistance of \( R_1 \) and \( R_2 \) in series**: \[ R_{series} = R_1 + R_2 = 4 + 6 = 10 \, \Omega \] 2. **Now, calculate the equivalent resistance of \( R_{series} \) and \( R_3 \) in parallel**: \[ \frac{1}{R_{total}} = \frac{1}{R_{series}} + \frac{1}{R_3} = \frac{1}{10} + \frac{1}{3} \] To combine these fractions, we find a common denominator: \[ \frac{1}{10} + \frac{1}{3} = \frac{3}{30} + \frac{10}{30} = \frac{13}{30} \] Therefore, the total resistance is: \[ R_{total} = \frac{30}{13} \approx 2.31 \, \Omega \] ### Conclusion In this example, we analyzed a combination circuit with both series and parallel components, calculating the total resistance step by step. If you have specific values or configurations in mind, please provide them, and I can help you analyze that particular circuit!