A \(40-\) W fluorescent lamp has power factor 0.85 and operates from the \(120-\mathrm{V}\) rms AC power line. How much current does it draw?

When discussing AC power systems, the concept of power factor is essential to understanding efficiency and electricity consumption. The power factor is a measure of how effectively electrical power is converted into useful work output. It is defined as the ratio of the real power flowing to the load, to the apparent power in the AC circuit.

Real power is the capacity of the circuit for performing work in a particular time. Apparent power, on the other hand, is the product of the current and voltage of the circuit. Due to energy being stored and then returned to the source by inductive and capacitive elements in the circuit, the apparent power is typically greater than the real power. The power factor is expressed as a number between 0 and 1 or as a percentage. High power factor indicates a more efficient AC power system, leading to less losses and a better use of electrical energy.

Alternating current (AC) is a type of electrical current that reverses direction periodically. Unlike direct current (DC), where the electric charge flows in a single direction, AC oscillates back and forth. This oscillation is particularly beneficial for the transmission of energy over long distances, which is why AC is the standard used for the majority of the world's electrical power supply.

The frequency of the alternating current, typically measured in cycles per second or Hertz (Hz), tells us how often the current changes direction in one second. Most residential systems operate at 60Hz in North America or 50Hz in Europe. Devices that operate on AC power are designed to work with these constantly changing currents, ensuring that electrical devices function properly.

Electric current is the orderly flow of electric charge carriers, which in most cases are electrons. The unit of electric current is the Ampere (A). A continuous and consistent movement of electrons through a conductor constitutes a current flow. In the context of AC power systems, the electric current periodically reverses direction.

Measuring current allows us to understand the amount of electricity being used by an appliance, such as the 40-W fluorescent lamp in the exercise. The current is a critical component in determining the operating characteristics and efficiency of your electrical devices and is an important measurement in calculating power consumption.

The concept of RMS (Root Mean Square) voltage is crucial when working with AC circuits. RMS voltage is a method of representing the effective voltage of an alternating current (AC). It corresponds to the amount of DC voltage that would produce the same power output in a resistive load.

The RMS value is particularly important because it gives a better representation of how much work the voltage can do. An AC voltage is usually given as an RMS value, which is why the power line voltage in the problem is specified as 120V rms. The RMS voltage is especially relevant when calculating power in AC circuits, like in our example where it is used to determine the amount of current drawn by the fluorescent lamp.