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 f_{1}, the inductive reactance will be:

XL1 = 2πf_{1}L ---(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 f_{1} = 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.