A string of 25 decorative lights has bulbs rated at 9.0 W,...

A string of 25 decorative lights has bulbs rated at 9.0 W, and the bulbs are connected in parallel. The string is connected to a $120 \mathrm{V}$ power supply. (a) What is the resistance of each of these lights? (b) What is the current through each bulb? (c) What is the total current coming from the power supply? (d) The string of bulbs has a fuse that will blow if the current is greater than 2.0 A. How many of the bulbs can you replace with $10.4 \mathrm{W}$ bulbs without blowing the fuse?

Key Concepts

Circuit Protection and Fuse Operation

A fuse serves as a safety device designed to protect an electrical circuit by breaking the connection if the current exceeds a specified limit. Understanding the operation of a fuse is vital for evaluating how changes in the load, such as replacing bulbs with ones that have a different power rating, could affect the total current and potentially trigger the fuse to blow. This concept is applied to assess modifications to the circuit while ensuring safe operation within the current limit prescribed by the fuse.

Parallel Circuit Analysis

In parallel circuits, all components are connected such that they share the same voltage across them, while the total current from the power supply is the sum of the individual currents through each component. This concept is crucial to understanding how the total current is calculated when multiple bulbs are connected in parallel, as each device draws its own current independently from the supply.

Ohm's Law

This law defines the relationship between voltage, current, and resistance in an electrical circuit, expressed as V = IR. It provides the fundamental basis for analyzing circuits by allowing the calculation of current when voltage and resistance are known, or vice versa. In the context of the problem, Ohm's Law is used to determine the current through each bulb based on the operating voltage and the calculated or given resistance.

Power in Resistive Circuits

The power dissipated in a resistive element is related to voltage and resistance through formulas such as P = V²/R or P = I²R. This concept is essential for finding the resistance of a lighting element when the power rating and voltage are known. In electric circuits, it helps determine how much energy is being converted into heat or light by each resistor or bulb.

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