Question

Differentiate between peak and rms values of alternating current. How are they related?

Answer 1

Alternating Current: Peak and RMS Values

1. Peak Value (\( I_0 \))

The peak value of an alternating current or voltage is its maximum magnitude in either direction within one cycle. It is also termed the maximum value.

Definition: The apex of the AC waveform during a cycle.

2. RMS Value (\( I_{\text{rms}} \))

The root mean square (rms) value of an alternating current is equivalent to the DC current that would generate identical heat in a specific resistor over the same duration as the AC.

Mathematical Relation:

The relationship between RMS current and peak current is:

\[ I_{\text{rms}} = \frac{I_0}{\sqrt{2}} \]

Likewise, for voltage, the RMS value relates to the peak voltage \( V_0 \) as:

\[ V_{\text{rms}} = \frac{V_0}{\sqrt{2}} \]

Conclusion:

The RMS value is significant as it signifies the effective AC current or voltage, enabling direct comparison with DC values concerning their heating capability in a resistor.