Understanding Electrical Current and Charge Flow: A Closer Look

The question of how much charge flows through the filament of a lamp when a certain amount of current is applied can often lead to confusion, especially when dealing with direct current (DC) versus alternating current (AC). Let's explore the different scenarios and clarify the concept of electrical charge flow.

The Basics: Coulomb and Current

First, it's essential to understand the basic units and definitions. 1 Coulomb (C) is the charge that passes through a point in a circuit when a current of 1 Ampere (A) flows for 1 second. This relationship is fundamental to understanding electrical charge and its movement in circuits.

Note: The Time Traveler's answer was incorrect because they provided the answer in terms of electron charge units (e) instead of coulombs (C).

DC Circuit Scenario

Consider a direct current (DC) circuit:

In a DC circuit, an electrical current flows from the positive terminal of the power supply through a conducting wire, through the filament, and back to the negative terminal. Here, the charge does flow through the filament.

If there is a current of 6 Amperes flowing for 1.75 seconds, the amount of charge that flows through the filament can be calculated as follows:

Charge (Q) Current (I) x Time (t)

Charge (Q) 6 A x 1.75 s 10.5 Coulombs

So, in this case, 10.5 Coulombs of charge flow through the filament in 1.75 seconds.

AC Circuit Scenario

In an alternating current (AC) circuit:

The current changes direction periodically, usually 50 or 60 times per second, depending on the frequency of the power supply.

For an AC light bulb, the electrons in the filament oscillate back and forth, but do not move from one end of the filament to the other.

Thus, in an ideal AC scenario, no net charge flows through the filament, and the charge enters and exits the filament repeatedly without flowing through it.

However, if we consider the moving charge within the filament, we can estimate the total charge present:

Let's assume an electron drift velocity of 4 mm/s in a filament 50 cm in length. With 8 Coulombs passing each point every second, we can estimate the total charge in the filament:

Total charge in the filament 50 cm / 4 mm * 8 C 1000 Coulombs.

Therefore, from this perspective, approximately 1000 Coulombs of charge is present in the filament.

The Nuances of Direct vs Alternating Current

The fundamental difference between DC and AC lies in the nature of the current flow:

DC current represents a steady flow, where a specific amount of charge flows through a point in the circuit over a unit of time.

AC current, on the other hand, does not involve a net flow of charge but instead oscillates. The AC rms (root mean square) current is defined as the DC current that would produce the same heating effect in a given resistance.

Thus, in an AC circuit, no net charge flows through the filament, but the current oscillates and carries charge at every moment.

Conclusion

The question, as formulated, is indeed a bit ambiguous and requires careful consideration of the circuit type (DC or AC). Understanding the nuances between DC and AC circuits is key to properly interpreting electrical flow and charge movement.

For DC circuits, we can calculate the exact amount of charge that flows through the filament based on the current and time. In AC circuits, the concept of charge movement differs significantly, leading to no net charge flow despite the oscillating current.

Regardless of the circuit type, the core concepts of electricity and current remain fundamental and essential in the study of physics and electrical engineering.

Keywords: Coulomb, electric current, electron charge, DC, AC