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 power dissipated in 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. Here, each bulb has a voltage of 120 V across it.
2. Use Ohm's Law to find the current through each bulb. Ohm's Law is given by \( I = \frac{V}{R} \), where \( I \) is the current, \( V \) is the voltage, and \( R \) is the resistance. Calculate the current through the 400Ω bulb and the 800Ω bulb separately.
3. For the 400Ω bulb, substitute \( V = 120 \text{ V} \) and \( R = 400 \Omega \) into the formula to find the current \( I_1 \).
4. For the 800Ω bulb, substitute \( V = 120 \text{ V} \) and \( R = 800 \Omega \) into the formula to find the current \( I_2 \).
5. Finally, calculate the power dissipated in each bulb using the formula \( P = IV \), where \( P \) is the power, \( I \) is the current through the bulb, and \( V \) is the voltage across the bulb. Calculate the power for both the 400Ω bulb and the 800Ω bulb using their respective currents and the voltage of 120 V.

Key Concepts

Ohm's Law

Ohm's Law states that the current through a conductor between two points is directly proportional to the voltage across the two points, and inversely proportional to the resistance. It is expressed as I = V/R, where I is the current, V is the voltage, and R is the resistance. This law is essential for calculating the current flowing through each bulb when connected in parallel.

Parallel Circuit

In a parallel circuit, components are connected across common points or junctions, providing multiple paths for the current to flow. The voltage across each component is the same, but the total current is the sum of the currents through each path. Understanding parallel circuits is crucial for determining how the voltage is distributed across the bulbs and how to calculate the current through each bulb.

Power Dissipation

Power dissipation in an electrical component is the rate at which it converts electrical energy into heat and other forms of energy. It is calculated using the formula P = VI, where P is the power, V is the voltage, and I is the current. Alternatively, in terms of resistance, it can be expressed as P = V^2/R for components in parallel. This concept is key to finding the power dissipated in each bulb.