# The inductive reactance of a coil at 100 Hz is 20 ohms. Its reactance at 1 kHz would be

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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

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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, XL = 20 Ω, we can write:

$\frac{20}{X_{L2}}=\frac{100}{1000}$

XL2 = 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.