For the Zener voltage regulation shown, determine the range of RL and IL that gives the stabilizer voltage of 10 V.

Question

For the Zener voltage regulation shown, determine the range of [latex]R_{L}[/latex] and [latex]I_{L}[/latex] that gives the stabilizer voltage of 10 V.

Accepted Answer

From the circuit, I = [latex]I_{Z} + I_{L}[/latex]
But from R, I =[latex]\frac{V_{in} – V_{o}}{R}=\frac{40 – 10}{1 × 10^{3}}[/latex] = 30 mA

When [latex]I_{L}[/latex] is minimum, [latex]I_{Z}[/latex] is maximum and vice versa.

I = [latex]I_{Zmax} + I_{Lmin}[/latex]
30 mA = 24 mA + [latex]I_{Lmin}[/latex]

Therefore, [latex]I_{Lmin}[/latex] = 6 mA
But [latex]I_{Lmin} =\frac{V_{o}}{R_{Lmax}}[/latex]

[latex]R_{Lmax} =\frac{V_{o}}{I_{Lmin}}=\frac{10}{6 × 10^{– 3}}[/latex] = 1.667 kΩ

and I = [latex]I_{Zmin} + I_{Lmax}[/latex]
30 mA = 5 mA + [latex]I_{Lmax}[/latex]
[latex]I_{Lmax}[/latex] = 25 mA
But [latex]I_{Lmax} =\frac{V_{o}}{R_{L min}}[/latex]

[latex]R_{Lmin} =\frac{V_{o}}{I_{Lmax}}=\frac{10}{25 × 10^{– 3}}[/latex]= 400 Ω

Hence, the range of [latex]I_{L}[/latex] is 6 mA to 25 mA and that of [latex]R_{L}[/latex] is 400 W to 1.667 kW.

Question 18.37: For the Zener voltage regulation shown, determine the range ...

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