A capacitor of capacitance C is connected across an AC voltage source of frequency f. If the frequency of the AC source is doubled while keeping the RMS voltage constant, how does the capacitive reactance X_C change?
Answer and explanation
Correct answer: C. It is halved (X_C' = X_C / 2)
.
- Step 1: The capacitive reactance of a capacitor is given by: .
- Step 2: Notice that is inversely proportional to frequency: .
- Step 3: When the frequency is doubled ():
- Step 4: Therefore, the capacitive reactance is halved.
Answer
It is halved (X_C' = X_C / 2)
Why not the others: 'It is doubled' confuses capacitive reactance with inductive reactance (which is directly proportional to frequency); 'It increases by a factor of 4' assumes an inverse-square dependence; 'It remains unchanged' overlooks frequency dependence entirely.
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