An alternating voltage source is described by the equation V(t) = 220√2 sin(100πt) V. What are the root-mean-square (RMS) voltage and the frequency of this AC supply?
Answer and explanation
Correct answer: C. Vrms = 220 V, f = 50 Hz
and .
.
.
- Step 1: The standard form of an alternating sinusoidal voltage is: , where is the peak voltage and is the angular frequency.
- Step 2: Comparing with the standard form:
- Step 3: The RMS voltage is calculated as: .
- Step 4: The frequency is related to angular frequency by :
Answer
Vrms = 220 V, f = 50 Hz
Why not the others: 'Vrms = 311 V, f = 100 Hz' reports peak voltage instead of RMS voltage and confuses with frequency; 'Vrms = 220 V, f = 100 Hz' forgets to divide by ; 'Vrms = 155.6 V, f = 50 Hz' divides by a second time.
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