Question
Download Solution PDFAn AC voltage is applied across a capacitor. If the frequency of the supply voltage is doubled, then the capacitive reactance will become:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCONCEPT:
Capacitive reactance:
- The capacitive reactance is the opposition offered by the capacitor in an AC circuit to the flow of ac current.
- Its SI unit is Ohm(Ω).
- The capacitive reactance is given as,
\(⇒ X_C=\frac{1}{ω C}=\frac{1}{2π fC}\)
Where ω = angular frequency, f = frequency of ac current and C = capacitance
Impedance:
- Impedance is essentially everything that obstructs the flow of electrons within an electrical circuit.
- For a pure capacitor, the capacitive reactance is equal to the impedance.
AC voltage applied to a capacitor:
- When an AC voltage is applied to a capacitor, the current in the circuit is given as,
\(⇒ I=\frac{V}{X_C}\)
- In a pure capacitor circuit, the current is ahead of the voltage by one-fourth of a period.
CALCULATION:
- We know that the capacitive reactance is given as,
\(⇒ X_C=\frac{1}{2π fC}\) -----(1)
Where f = frequency of ac current and C = capacitance
For case 1:
\(⇒ X_C=\frac{1}{2π fC}\) -----(2)
For case 2: (f' = 2f)
\(⇒ X_C^{'}=\frac{1}{2π f'C}\)
\(⇒ X_C^{'}=\frac{1}{2π \times2fC}\)
\(⇒ X_C^{'}=\frac{1}{2}\times\frac{1}{2πfC}\) -----(3)
By equation 2 and equation 3,
\(⇒ X_C^{'}=\frac{X_C}{2}\)
- Hence option 2 is correct.
Last updated on Jul 4, 2025
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