Light Bulbs in Series and in Parallel. Two light bulbs have constant resistances of 400Ω and 800Ω. The two light bulbs are now connected in parallel across the 120 V line. Find the current through each bulb.

Verified step by step guidance

1. First, understand that when resistors (or light bulbs in this case) are connected in parallel, the voltage across each resistor is the same as the source voltage. Therefore, each bulb experiences the full 120 V.
2. Use Ohm's Law to find the current through each bulb. Ohm's Law is given by the formula: $I=\frac{V}{R}$, where $I$ is the current, $V$ is the voltage, and $R$ is the resistance.
3. Calculate the current through the 400Ω bulb using Ohm's Law: $I=\frac{120 V}{400}$. This will give you the current through the 400Ω bulb.
4. Similarly, calculate the current through the 800Ω bulb using Ohm's Law: $I=\frac{120 V}{800}$. This will give you the current through the 800Ω bulb.
5. Remember that in a parallel circuit, the total current supplied by the source is the sum of the currents through each parallel branch. However, for this problem, you are only asked to find the current through each bulb individually.

Key Concepts

Ohm's Law

Ohm's Law is a fundamental principle in electronics that relates voltage (V), current (I), and resistance (R) in a circuit. It is expressed as V = IR, meaning the voltage across a resistor is equal to the product of the current flowing through it and its resistance. This law is essential for calculating the current through each bulb when connected in parallel.

Parallel Circuit

In a parallel circuit, components are connected across the same voltage source, allowing multiple paths for current to flow. Each component receives the full voltage of the source, and the total current is the sum of the currents through each component. Understanding parallel circuits is crucial for determining how the 120-V line affects each bulb individually.

Current Division Rule

The current division rule helps calculate the current through individual components in a parallel circuit. It states that the current through a resistor in parallel is inversely proportional to its resistance, given the total current and the resistances involved. This concept is vital for finding the current through each bulb with known resistances and applied voltage.