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The value of the resistor, $$R_S$$, needed in the DC voltage regulator circuit shown here, equals:
According to Kirchhoff's Current Law, the total current $$I_S$$ flowing through the series resistor $$R_S$$ is the sum of the current through the Zener diode ($$I_Z$$) and the current through the load ($$I_L$$).
$$I_S = I_Z + I_L$$
$$I_S = nI_L + I_L = (n + 1)I_L$$
$$V_{R_S} = V_i - V_L$$
$$R_S = \frac{V_{R_S}}{I_S}$$
$$R_S = \frac{V_i - V_L}{(n + 1)I_L}$$
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