What is the relationship between the electrical resistance and the power of a lamp?
The electrical resistance of a 100-Watt lamp glowing brighter than a 25-Watt lamp would be less. This is due to the concept that resistance is inversely proportional to power in electrical circuits.
Understanding Electrical Resistance and Power
Electrical resistance is a fundamental concept in the field of physics and electrical engineering. It refers to the opposition that a material offers to the flow of electric current. The unit of resistance is ohms (Ω), and it is represented by the symbol "R".
When it comes to power consumption in electrical devices such as lamps, the power is directly related to the brightness of the lamp. Power is the rate at which energy is transferred by an electric circuit and it is measured in watts (W).
The relationship between electrical resistance and power can be explained through Ohm's Law, which 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. Mathematically, Ohm's Law is represented as I = V/R, where I is the current, V is the voltage, and R is the resistance.
In the case of a 100-Watt lamp and a 25-Watt lamp, the concept of electrical resistance comes into play. The electrical resistance is inversely proportional to the power of the lamp, given a constant voltage. If the 100-Watt lamp glows brighter than the 25-Watt lamp, it consumes more power for the same voltage, therefore the resistance must be less.
Here's a simple example to illustrate this concept: Imagine electricity flowing through a pipe, where resistance is analogous to the width of the pipe. A wider pipe (less resistance) allows more water (electricity) to flow through it. Similarly, a 100-Watt lamp, which is brighter and consumes more power, would have a lower resistance, akin to a wider pipe, than a 25-Watt lamp.
In conclusion, the electrical resistance of a 100-Watt lamp is less than that of a 25-Watt lamp due to the higher power consumption and brightness of the 100-Watt lamp.