Question

The value of the alternating current which is equal to the DC current that gives the same heating effect over a fixed period of time is called:

• A. Average current
• B. Peak current
• C. RMS current
• D. Peak-to-peak current

Hint:

RMS current represents the effective heating value of AC and equals \( \dfrac{I_{\text{peak}}}{\sqrt{2}} \) for sine waves.

Answer 1

The Correct Option is C

The correct answer to the question is RMS current.

Explanation:

In electrical engineering, particularly in the study of AC circuits, the term used to describe an AC current that delivers the same amount of heating effect in a resistor as an equivalent DC current is called the Root Mean Square (RMS) current. The RMS value is a statistical measure of the magnitude of a varying quantity and is especially useful in contexts like AC where values oscillate over time.

Mathematically, if \( I(t) \) is the instantaneous current as a function of time, the RMS current \( I_{\text{RMS}} \) over one period is calculated using the formula:

\[ I_{\text{RMS}} = \sqrt{\frac{1}{T} \int_{0}^{T} [I(t)]^{2} \, dt} \]

This definition allows the RMS value to be directly comparable to DC values, aiding in power calculations and other analyses involving AC circuits. None of the other given options—Average current, Peak current, or Peak-to-peak current—provide the same equivalence to constant DC heating power, thus confirming that the RMS current is the correct answer.