You have a special light bulb with a very delicate wire filament. The wire will break if the current in it ever exceeds 1.50 A, even for an instant. What is the largest root-mean-square current you can run through this bulb?

Verified step by step guidance

1. Understand the relationship between the maximum current and the root-mean-square (RMS) current. The RMS current is a statistical measure of the magnitude of a varying current and is particularly useful for alternating currents (AC).
2. Recognize that for a sinusoidal AC current, the peak or maximum current ( ext{I}_{ ext{max}}) is related to the RMS current ( ext{I}_{ ext{RMS}}) by the equation ext{I}_{ ext{max}} = ext{I}_{ ext{RMS}} \times \sqrt{2}.
3. Given that the wire will break if the current exceeds 1.50 A, set ext{I}_{ ext{max}} equal to 1.50 A in the equation from step 2.
4. Rearrange the equation to solve for ext{I}_{ ext{RMS}}: ext{I}_{ ext{RMS}} = \frac{ ext{I}_{ ext{max}}}{\sqrt{2}}.
5. Substitute ext{I}_{ ext{max}} = 1.50 A into the equation to find the largest RMS current that can be safely used without breaking the filament.

Key Concepts

Root-Mean-Square (RMS) Current

Root-mean-square (RMS) current is a statistical measure of the magnitude of a varying current. It is defined as the square root of the average of the squares of the instantaneous values over one complete cycle. For alternating current (AC), the RMS value is particularly useful because it provides a way to express the effective value of the current, which can be used to calculate power in resistive circuits.

Current Limitations

Current limitations refer to the maximum allowable current that can safely pass through a conductor or device without causing damage. In this case, the delicate wire filament of the light bulb can only handle a maximum current of 1.50 A. Exceeding this limit, even momentarily, can lead to overheating and breakage of the filament, which is critical for the bulb's operation.

AC vs. DC Current

AC (alternating current) and DC (direct current) are two types of electrical current. AC current changes direction periodically, while DC current flows in a single direction. The RMS current is particularly relevant in AC circuits, as it allows for the comparison of AC to DC in terms of power delivery. Understanding the type of current is essential for determining how to apply the current limit in practical scenarios.