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. (g) In each situation, which of the two bulbs glows the brightest?

Verified step by step guidance

1. Calculate the total resistance when the bulbs are connected in series. Use the formula for resistors in series: R_{total} = R_1 + R_2, where R_1 and R_2 are the resistances of the two bulbs.
2. Determine the current flowing through the circuit when the bulbs are in series using Ohm's Law, I = V / R_{total}, where V is the voltage of the line.
3. Calculate the power dissipated by each bulb when in series using the formula P = I^2 imes R, where I is the current calculated in the previous step and R is the resistance of each bulb. The bulb with the higher power dissipation glows brighter.
4. Calculate the total resistance when the bulbs are connected in parallel using the formula for resistors in parallel: 1/R_{total} = 1/R_1 + 1/R_2.
5. Determine the power dissipated by each bulb when in parallel using the formula P = V^2 / R, where V is the voltage of the line and R is the resistance of each bulb. Again, the bulb with the higher power dissipation glows brighter.

Key Concepts

Ohm's Law

Ohm's Law states that the current (I) flowing through a conductor between two points is directly proportional to the voltage (V) across the two points and inversely proportional to the resistance (R) of the conductor. This relationship is expressed as V = IR. Understanding this law is crucial for analyzing how voltage, current, and resistance interact in electrical circuits, particularly when determining the brightness of light bulbs based on their resistances.

Series and Parallel Circuits

In a series circuit, components are connected end-to-end, so the same current flows through each component, while the total voltage is divided among them. In contrast, in a parallel circuit, components are connected across the same voltage source, allowing each component to operate independently with the same voltage across them. This distinction is essential for understanding how the configuration of light bulbs affects their brightness, as the current distribution varies significantly between series and parallel arrangements.

Power Dissipation in Resistors

The power (P) dissipated by a resistor can be calculated using the formula P = I^2R, where I is the current through the resistor and R is its resistance. In the context of light bulbs, the brightness is related to the power they dissipate; the bulb that dissipates more power will glow brighter. This concept is vital for comparing the brightness of the bulbs in both series and parallel configurations, as it directly relates to the current and resistance of each bulb.