In an AC circuit, if the voltage is given by V(t) = 100 sin(100t), what is the R

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Question: In an AC circuit, if the voltage is given by V(t) = 100 sin(100t), what is the RMS voltage? (2023)

Options:

Correct Answer: 70.7 V

Exam Year: 2023

Solution:

The RMS voltage is V_rms = V0/√2 = 100/√2 = 70.7 V.

In an AC circuit, if the voltage is given by V(t) = 100 sin(100t), what is the RMS voltage? (2023)

In an AC circuit, if the voltage is given by V(t) = 100 sin(100t), what is the RMS voltage? (2023)

Step 1: Identify the given voltage function, which is V(t) = 100 sin(100t).
Step 2: Recognize that the maximum voltage (V0) in this function is 100 volts.
Step 3: Understand that the RMS (Root Mean Square) voltage can be calculated using the formula V_rms = V0 / √2.
Step 4: Substitute the maximum voltage into the formula: V_rms = 100 / √2.
Step 5: Calculate the value of 100 / √2, which is approximately 70.7 volts.
Step 6: Conclude that the RMS voltage is 70.7 V.

RMS Voltage Calculation – The calculation of the root mean square (RMS) voltage from the peak voltage in an AC circuit.
AC Voltage Representation – Understanding the sinusoidal representation of AC voltage and its parameters.