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The value of ...

Question

The value of the resistor, $R_{S}$ , needed in the dc voltage regulator circuit shown here is equal to :

A

\frac{(V_{i} - V_{L})}{n I_{L})}

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B

\frac{(V_{i} + V_{L})}{n I_{L}}

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C

\frac{(V_{i} - V_{L})}{(n + 1) I_{L}}

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D

\frac{(V_{i} - V_{L})}{(n + 1) I_{L}}

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Solution

The correct option is C $\frac{(V_{i} - V_{L})}{(n + 1) I_{L}}$
Voltage across $R_{s} = V_{i} - V_{l}$
Current across $R_{s} = n I_{l} + I_{l} = I_{l} (n + 1)$
$- R_{s} = \frac{V_{i} - V_{l}}{I_{l} (n + 1)}$

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