If 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

Question

Question

This question was previously asked in

ALP CBT 2 Electrician Official Paper (Held On: 23 Jan 2019 Shift 3)

Answer 1

Concept:

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, \({X_C} = \frac{1}{{2π \times 50\times 1\times 10^{-6}}}\)

∴ X_C = 3183.09 Ω