The inductive reactance of a coil is ' $\mathrm{X}_{\mathrm{L}}$ '. If the inductance of a coil is tripled…

The inductive reactance of a coil is ' $\mathrm{X}_{\mathrm{L}}$ '. If the inductance of a coil is tripled and frequency of a.c. supply, is doubled, then the new inductive reactance will be
  1. $\frac{2}{3} X_L$
  2. $\frac{3}{2} X_L$
  3. $\frac{1}{6} X_L$
  4. $6 X_L$

Solution

$\begin{aligned} \mathrm{X}_{\mathrm{L}} & =\omega \mathrm{L}=2 \pi \mathrm{fL} \\ \mathrm{f}_{\text {new }} & =2 \mathrm{f} \text { and } \mathrm{L}_{\text {new }}=3 \mathrm{~L} \\ \therefore \quad \mathrm{X}_{\mathrm{L}}^{\prime} & =2 \pi(2 \mathrm{f}) 3 \mathrm{~L} \\ & =6 \times 2 \pi \mathrm{fL}=6 \mathrm{X}_{\mathrm{L}}\end{aligned}$ /

Asked in: MHT CET 2023 (10 May Shift 1)

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