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Two series resistors are connected to an ac source. If there are 7.5 V rms across one resistor and 4.2 V rms across the other, the peak source voltage is
Answer & Solution
Answer: Option
A
Solution:
Understanding the Problem:
We have two resistors in series connected to an AC voltage source.
We know the RMS (Root Mean Square) voltage across each resistor.
We need to find the peak voltage of the source.
Key Concepts:
RMS Voltage: This is the effective voltage of an AC signal, equivalent to a DC voltage that would produce the same heating effect.
Peak Voltage: This is the maximum voltage reached by the AC signal during each cycle. The relationship between peak voltage (Vpeak) and RMS voltage (Vrms) is: Vpeak = Vrms * √2
Series Circuit: In a series circuit, the current is the same through all components. The voltages across the resistors add up to the source voltage.
Steps to Solve:
1. Find the total RMS voltage: Since the resistors are in series, the total RMS voltage is the sum of the RMS voltages across each resistor. So, Vrms(total) = 7.5 V + 4.2 V = 11.7 V
2. Calculate the peak voltage: Use the formula Vpeak = Vrms * √2. So, Vpeak = 11.7 V * √2 ≈ 11.7 V * 1.414 ≈ 16.54 V
Therefore, the correct answer is Option A: 16.54 V
We have two resistors in series connected to an AC voltage source.
We know the RMS (Root Mean Square) voltage across each resistor.
We need to find the peak voltage of the source.
Key Concepts:
RMS Voltage: This is the effective voltage of an AC signal, equivalent to a DC voltage that would produce the same heating effect.
Peak Voltage: This is the maximum voltage reached by the AC signal during each cycle. The relationship between peak voltage (Vpeak) and RMS voltage (Vrms) is: Vpeak = Vrms * √2
Series Circuit: In a series circuit, the current is the same through all components. The voltages across the resistors add up to the source voltage.
Steps to Solve:
1. Find the total RMS voltage: Since the resistors are in series, the total RMS voltage is the sum of the RMS voltages across each resistor. So, Vrms(total) = 7.5 V + 4.2 V = 11.7 V
2. Calculate the peak voltage: Use the formula Vpeak = Vrms * √2. So, Vpeak = 11.7 V * √2 ≈ 11.7 V * 1.414 ≈ 16.54 V
Therefore, the correct answer is Option A: 16.54 V