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A Zener of power rating $1\, W$ is to be used as a voltage regulator. If zener has a breakdown of $5\,V$ and it has to regulate voltage which fluctuated between $3\,V$ and $7\,V$, what should be the value of $R_s$ for safe operation (See figure) ?
Solution
$\quad \mathrm{P}=\mathrm{V}_{\mathrm{Z} \mathrm{Z}} \mathrm{Z}$ $\therefore(\mathrm{P})_{\max }=\mathrm{V}_{\mathrm{Z}}\left(\mathrm{I}_{\mathrm{Z}}\right)_{\max .} \quad\left(\because \mathrm{V}_{\mathrm{Z}}=\right.$ constant $)$
$\therefore 1=5 \times\left(\mathrm{I}_{\mathrm{Z}}\right)_{\max .}$ $\therefore\left(\mathrm{I}_{\mathrm{Z}}\right)_{\max .}=\frac{1}{5}=0.2 \mathrm{~A}$ Here, $\quad v_{i}=\mathrm{I}_{\mathrm{Z}} \mathrm{R}_{\mathrm{S}}+\mathrm{V}_{\mathrm{Z}}$ $\therefore\left(\mathrm{V}_{i}\right)_{\max }=\left(\mathrm{I}_{\mathrm{Z}}\right)_{\max .} \mathrm{R}_{\mathrm{S}}+\mathrm{V}_{\mathrm{Z}}$
$\therefore 7=0.2 \mathrm{R}_{\mathrm{S}}+5$
$\therefore \mathrm{R}_{\mathrm{S}}=\frac{7-5}{0.2}=\frac{2}{0.2}=10 \Omega$
