An AC source of angular frequency ω is connected to a resistor R and a capacitor C in series. The maximum current measured is Imax. While the same maximum emf is maintained, the angular frequency is changed to ω/3. The measured current is now I/2. Determine the ratio of the capacitive reactance to the resistance at the initial frequency ω.
The ratio of the capacitive reactance to the resistance at the initial frequency.
Answer to Problem 60PQ
The ratio of the capacitive reactance to the resistance at the initial frequency is
Explanation of Solution
Write the expression to calculate the potential drop across the capacitor.
Here,
Write the expression for capacitive reactance.
Here,
Write the expression for the potential difference across the resistor.
Here,
Write the expression for the emf across the
Here,
Substitute
Rearrange equation (V) to get the expression for
The relation for the maximum current is,
Substitute
Substitute
Equate equation (VIII) and (XI)
Square both side of the equation and substitute
Sole further.
Conclusion:
Therefore, the ratio of the capacitive reactance to the resistance at the initial frequency is
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Chapter 33 Solutions
Physics for Scientists and Engineers: Foundations and Connections
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