Question
Download Solution PDFIf a resistance of 10 ohms and a capacitance of 1 μF is connected across a 230 V, 50 Hz AC supply, the capacitive reactance of the circuit is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Inductive reactance:
Inductive reactance (XL) is given by:
XL = ωL
ω = frequency in radian/sec which can be written as:
ω = 2πf
XL = ωL = 2πfL
Where,
f = frequency in Hz
L = value of inductor in Henry
From the above, we conclude that:
XL ∝ f (for a constant L)
The inductive reactance is directly proportional to frequency.
Capacitive reactance:
Capacitive reactance is given by:
\({X_C} = \frac{1}{{ω C}}\)
With ω = 2πf
\({X_C} = \frac{1}{{2π fC}}\)
\({X_C} \propto \frac{1}{{ f}}\)
The capacitive reactance is inversely proportional to the frequency.
Where, C = capacitance value in Farad
Calculation:
Given that, capacitance (C) = 1 μF
Frequency (f) = 50 Hz
Capacitive reactance, \({X_C} = \frac{1}{{2π \times 50\times 1\times 10^{-6}}}\)
∴ XC = 3183.09 Ω
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