A) 0.16 H
B) 0.22 H
C) 2.2 H
D) 1.6 H
Correct Answer: A
Solution :
In a coil the product of angular frequency\[(\omega )\]and inductance (L) is known as the reactance of the coil or inductive reactance and is denoted by\[{{X}_{L}}\]. Thus, \[{{X}_{L}}=\omega L=2\pi fL\] where\[f\]is frequency. Putting the numerical values from the. question, we have \[{{X}_{L}}=50\,\Omega ,f=50\,cps\] \[\therefore \] \[L=\frac{{{X}_{L}}}{\omega }=\frac{{{X}_{L}}}{2\pi f}=\frac{50}{2\pi \times 50}\] \[=\frac{1}{2\times 3.14}=0.16\,H\]
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