Question: In an AC circuit, if the voltage is V(t) = 120 sin(ωt), what is the RMS voltage? (2017)
Options:
120 V
60 V
84.85 V
100 V
Correct Answer: 84.85 V
Solution:
RMS voltage V_rms = V_peak / √2 = 120 / √2 = 84.85 V.
In an AC circuit, if the voltage is V(t) = 120 sin(ωt), what is the RMS voltage?
Practice Questions
Q1
In an AC circuit, if the voltage is V(t) = 120 sin(ωt), what is the RMS voltage? (2017)
120 V
60 V
84.85 V
100 V
Questions & Step-by-Step Solutions
In an AC circuit, if the voltage is V(t) = 120 sin(ωt), what is the RMS voltage? (2017)
Step 1: Identify the peak voltage from the given voltage function V(t) = 120 sin(ωt). The peak voltage (V_peak) is 120 volts.
Step 2: Understand that the RMS (Root Mean Square) voltage can be calculated using the formula: V_rms = V_peak / √2.
Step 3: Substitute the peak voltage into the formula: V_rms = 120 / √2.
Step 4: Calculate the value of √2, which is approximately 1.414.
Step 5: Divide 120 by 1.414 to find the RMS voltage: V_rms ≈ 84.85 volts.
RMS Voltage Calculation – The calculation of RMS (Root Mean Square) voltage from the peak voltage in an AC circuit, using the formula V_rms = V_peak / √2.
Understanding AC Voltage Waveforms – Recognizing the sinusoidal nature of AC voltage and how it relates to peak and RMS values.
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