Physics - EMI/AC Question with Solution | TestHub

From the diagram given,

Angular frequency $\omega =100rad{\text{s}}^{-1}$ and $V_{rm\text{s}}=\frac{V_0}{\sqrt{2}}=\frac{20\sqrt{2}}{\sqrt{2}}=20\mathrm{V}$.

Now, $X_L=\omega L=100\times 100\times 10^{-3}=10\Omega$ and $X_C=\frac{1}{\omega \mathrm{C}}=\frac{1}{100\times 100\times 10^{-6}}=100\Omega$

$\left|\left(X_L-X_C\right)\right|=\left|10-100\right|=90\Omega$The impedance of the circuit,

$Z=\sqrt{{\left(X_L-X_C\right)}^2+R^2}=\sqrt{{\left(90\right)}^2+{\left(120\right)}^2}=150\Omega$The current in the circuit,

$$i_{mrs}=\frac{V_{rms}}{Z}=\left(\frac{20}{150}\right)\mathrm{A}$$

Power factor $\cos \varphi =\frac{R}{Z}$

Now

$$\begin{gathered} \left(V_{rm\text{s}}{i}_{rm\text{s}}\cos \varphi \right)\Delta t=m\text{s}\left(\Delta \mathrm{T}\right) \\ \Rightarrow \Delta t=\frac{m\text{s}\left(\Delta \mathrm{T}\right)}{V_{rm\text{s}}\times \frac{V_{rm\text{s}}}{Z}\times \frac{R}{Z}}=\frac{m\text{s}\left(\Delta \mathrm{T}\right)Z^2}{{\left(V_{rm\text{s}}\right)}^2\times R}=\frac{2\times 16\times 22500}{400\times 120}=15\text{s} \end{gathered}$$

$\Rightarrow \Delta t=15\text{s}$