Differentiate between peak and rms values of alternating current. How are
they related?
Solution and Explanation
Peak Value and RMS Value of Alternating Current
1. Peak Value (\( I_0 \))
The peak value of an alternating current (or voltage) is the maximum value attained in either direction during one cycle. It is also called the maximum value.
Definition: The highest point reached by the AC waveform during a cycle.
2. RMS Value (\( I_{\text{rms}} \))
The root mean square (rms) value of an alternating current is defined as the value of a steady (DC) current that would produce the same amount of heat in a given resistor in the same time as the AC does.
Mathematical Relation:
The RMS value for current is related to the peak value as:
\[ I_{\text{rms}} = \frac{I_0}{\sqrt{2}} \]
Similarly, for voltage, the RMS value is related to the peak voltage \( V_0 \) as:
\[ V_{\text{rms}} = \frac{V_0}{\sqrt{2}} \]
Conclusion:
The RMS value is particularly useful because it represents the effective value of an alternating current or voltage, which can be directly compared to a DC value in terms of its ability to produce heat in a resistor.
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