Question
In the given circuit the potential difference across resistance is $54\,V$ and power consumed by it is $16\,W$. If $AC$ frequency is $60\,Hz$ find the value of $L$......$H$
✓
Answer
a
$\mathrm{V}_{\mathrm{R}}^{2}+\mathrm{V}_{\mathrm{L}}^{2}=120^{2}$
$\mathrm{V}_{\mathrm{R}}^{2}+\mathrm{V}_{\mathrm{L}}^{2}=120^{2}$
$\mathrm{V}_{\mathrm{L}}=\sqrt{120^{2}-54^{2}}=107 \mathrm{V}$
$\because \mathrm{V}_{\mathrm{R}^{i}}=\mathrm{P} \quad \mathrm{i}=\frac{16}{54} \mathrm{A}$
Now $\mathrm{i} 2 \pi \mathrm{fL}=\mathrm{V}_{\mathrm{L}}$
$\Rightarrow \frac{16}{54} \times 2 \times \pi \times 60 \mathrm{L}=107$
$\Rightarrow \mathrm{L}=0.96 \mathrm{\,H} \approx 1 \mathrm{\,H}$
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