A capacitor and an inductor are connected to A.C. supply. If we double the frequency of A.C. supply then the effect on reactance of capacitor XC and reactance of inductor XL will be:
Correct answer: D. XL is doubled and XC reduces to half
- A. Both XC and XL are doubled
- B. Both XC and XL are halved
- C. XC is doubled and XL reduces to half
- D. XL is doubled and XC reduces to half
- E. Both XC and XL are unchanged
Explanation
The reactance of a capacitor is given by: Xc = 1/ (2πfC) where f is the frequency of the AC supply, and C is the capacitance of the capacitor. On doubling the frequency of the AC supply, the reactance of the capacitor becomes: X'c = 1/ (2π(2f)C) = Xc/2 Therefore, the reactance of the capacitor is halved when the frequency is doubled. The reactance of an inductor is given by: XL = 2πfL where L is the inductance of the inductor. On doubling the frequency of the AC supply, the reactance of the inductor becomes: X'L = 2π(2f)L = 2XL Therefore, the reactance of the inductor is doubled when the frequency is doubled.
This question appeared on the NUMS 2019 (cancelled sitting) paper, which you can sit online with every answer explained.
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About AC Through Resistor, Capacitor and Inductor
Alternating current through a resistor, capacitor and inductor involves phase relationships between voltage and current, reactance, impedance and energy transfer. A resistor keeps voltage and current in phase, while a capacitor and inductor produce opposite phase shifts, a distinction used in circuit diagrams and numerical calculations.
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