Physics - EMI/AC Question with Solution | TestHub

Current$\mathit{\text{I}}=\frac{\mathit{\text{E}}}{\mathit{\text{Z}}}$

where$\mathit{\text{E}}=\sqrt{{\mathit{\text{V}}}_{\mathit{\text{R}}}^2+{\left({\mathit{\text{V}}}_{\mathit{\text{L}}}-{\mathit{\text{V}}}_{\mathit{\text{C}}}\right)}^2}$

$\mathit{\text{Z}}=\sqrt{{\mathit{\text{R}}}^2+{\left({\mathit{\text{X}}}_{\mathit{\text{L}}}-{\mathit{\text{X}}}_{\mathit{\text{C}}}\right)}^2}$


At resonance,${\mathit{\text{X}}}_{\mathit{\text{L}}}={\mathit{\text{X}}}_{\mathit{\text{C}}}$

$\therefore$$\mathit{\text{Z}}=\mathit{\text{R}}$

Again at resonance,${\mathit{\text{V}}}_{\mathit{\text{L}}}={\mathit{\text{V}}}_{\mathit{\text{C}}}$

$\therefore$$\mathit{\text{E}}={\mathit{\text{V}}}_{\mathit{\text{R}}}$

$\therefore$$\mathit{\text{I}}=\frac{{\mathit{\text{V}}}_{\mathit{\text{R}}}}{\mathit{\text{R}}}=\frac{\text{100}}{1\times {\text{10}}^3}=$$\text{0.1}\text{ A}$

$\therefore$${\mathit{\text{V}}}_{\mathit{\text{L}}}=\mathit{\text{I}}\mathit{\text{L}}\omega =\frac{\mathit{\text{I}}}{\mathit{\text{C}}\omega }=\frac{\text{0.1}}{\left(2\times {\text{10}}^{-6}\right)\times \left(\text{200}\right)}$

$\therefore$${\mathit{\text{V}}}_{\mathit{\text{L}}}=\text{250 V}$.