Question

The inductive reactance of a coil at 100 Hz is 20 ohms. Its reactance at 1 kHz would be
1. 2
2. 10
3. 40
4. 200

Answer 1

Correct Answer - Option 4 : 200

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

f  = frequency in Hz

L = value of inductor in Henry

Calculation:

For a frequency of f₁, the inductive reactance will be:

XL1 = 2πf₁L  ---(1)

Similarly, for some other frequency, the inductive reactance wil be:

XL2 = 2πf2L   ---(2)

Dividing both the frequencies, we get:

\(\frac{X_{L1}}{X_{L2}}=\frac{2\pi f_1L}{2\pi f_2L}\)

\(\frac{X_{L1}}{X_{L2}}=\frac{f_1}{f_2}\)

With f₁ = 100 Hz, X_L = 20 Ω, we can write:

\(\frac{20}{X_{L2}}=\frac{100}{1000}\)

X_L2 = 200 Ω

Important Points:

The capacitive reactance for a capacitor operating in a particular frequency 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.