AP EAMCET · PHYSICS · Alternating Current

Capacitive reactance of a capacitor in an $A C$ circuit is $3 kΩ$ . If this capacitor is connected to a new $A C$ source of double frequency, the capacitive reactance will become

A $1.5 kΩ$
B $3 kΩ$
C $6 kΩ$
D $5.2 kΩ$

Verified Solution

Answer & Solution

Correct Answer

(A) $1.5 kΩ$

Step-by-step Solution

Detailed explanation

Capacitive reactance is given by, Xc=12πfC. Clearly, if the frequency of the AC source is doubled then capacitive reactance will be halved, which is 1.5 kΩ.

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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Capacitive reactance of a capacitor in an AC circuit is 3 kΩ. If this capacitor is connected to a new AC source of double frequency, the capacitive reactance will become

Step-by-step Solution

Capacitive reactance of a capacitor in an $A C$ circuit is $3 kΩ$ . If this capacitor is connected to a new $A C$ source of double frequency, the capacitive reactance will become