Light Bulbs in Series and in Parallel. Two light bulbs have constant resistances of 400Ω and 800Ω. The two light bulbs are connected in series across a 120 V line. Afterwards, the two light bulbs are connected in parallel across the 120 V line. In which situation is there a greater total light output from both bulbs combined?

Verified step by step guidance

1. Understand the concept of series and parallel circuits: In a series circuit, the current is the same through each component, while in a parallel circuit, the voltage across each component is the same.
2. Calculate the total resistance in the series circuit: The total resistance \( R_{total} \) in a series circuit is the sum of the individual resistances. Use the formula \( R_{total} = R_1 + R_2 \), where \( R_1 = 400 \Omega \) and \( R_2 = 800 \Omega \).
3. Determine the current in the series circuit: Use Ohm's Law \( I = \frac{V}{R} \) to find the current \( I \) through the series circuit, where \( V = 120 \text{ V} \) and \( R = R_{total} \).
4. Calculate the power output in the series circuit: The power \( P \) dissipated by each bulb can be calculated using \( P = I^2 R \). Calculate the power for each bulb and sum them to find the total power output in the series circuit.
5. Calculate the power output in the parallel circuit: In a parallel circuit, each bulb has the same voltage across it. Use \( P = \frac{V^2}{R} \) to calculate the power for each bulb individually, where \( V = 120 \text{ V} \). Sum the power outputs to find the total power output in the parallel circuit.

Key Concepts

Ohm's Law

Ohm's Law is a fundamental principle in physics that relates voltage (V), current (I), and resistance (R) in an electrical circuit through the equation V = IR. This law is crucial for calculating the current flowing through each light bulb when they are connected in series or parallel, as it helps determine the power output and thus the light intensity.

Series and Parallel Circuits

In a series circuit, components are connected end-to-end, so the same current flows through each component, but the total voltage is divided among them. In a parallel circuit, components are connected across the same voltage source, so each component receives the full voltage, but the total current is divided. Understanding these configurations is essential for analyzing how the light bulbs behave in each setup.

Power in Electrical Circuits

Power in an electrical circuit is given by the formula P = VI, where P is power, V is voltage, and I is current. Alternatively, it can be expressed as P = I^2R or P = V^2/R. This concept is key to determining the light output of the bulbs, as power is directly related to the brightness of the bulbs. Comparing power in series and parallel configurations will reveal which setup produces greater light output.