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Simple Circuit

The value of ...

Question

The value of the resistor, $R_{S}$ , needed in the DC voltage regulator circuit shown here, equals

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

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

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

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

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Solution

The correct option is C $\frac{(V_{i} - V_{L})}{(n + 1) I_{L}}$
Total current in resistance $R_{S}$ $I = n I_{L} + I_{L} = (n + 1) I_{L}$
Voltage across $R_{S}$ is $V_{S} = V_{i} - V_{L}$
$∴ R_{S} = \frac{V_{S}}{I} = \frac{V_{i} - V_{L}}{(n + 1) I_{L}}$

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