The figure represents a voltage regulator circuit using a Zener diode. The breakdown voltage of the Zener…

The figure represents a voltage regulator circuit using a Zener diode. The breakdown voltage of the Zener diode is $6\mathrm{ }\mathrm{V}$ and the load resistance is, ${\mathrm{R}}_{\mathrm{L}}=4\mathrm{ }\mathrm{k}\mathrm{\Omega }$ . The series resistance of the circuit is ${\mathrm{R}}_{\mathrm{i}}=1\mathrm{ }\mathrm{k}\mathrm{\Omega }$ . If the battery voltage ${\mathrm{V}}_{\mathrm{B}}$ varies from $8\mathrm{ }\mathrm{V}\mathrm{ }$ to $\mathrm{ }16\mathrm{ }\mathrm{V}$ , what are the minimum and maximum values of the current through Zener diode?

1. $0.5\mathrm{ }\mathrm{m}\mathrm{A};\mathrm{ }6\mathrm{ }\mathrm{m}\mathrm{A}$
2. $1\mathrm{ }\mathrm{m}\mathrm{A};\mathrm{ }8.5\mathrm{ }\mathrm{m}\mathrm{A}$
3. $0.5\mathrm{ }\mathrm{m}\mathrm{A};\mathrm{ }8.5\mathrm{ }\mathrm{m}\mathrm{A}$
4. $1.5\mathrm{ }\mathrm{m}\mathrm{A};\mathrm{ }8.5\mathrm{ }\mathrm{m}\mathrm{A}$

Solution

For ${\mathrm{V}}_0=8\mathrm{V}$

$8\mathrm{ }V-1000\mathrm{ }{\mathrm{i}}_0=6\mathrm{ }V$
${\mathrm{i}}_0=2\mathrm{ }\mathrm{m}\mathrm{A}$
${\mathrm{i}}_0-{\mathrm{i}}_1=\frac{6}{4000}=1.5\mathrm{ }\mathrm{m}\mathrm{A}$
${\mathrm{i}}_1=0.5\mathrm{ }\mathrm{m}\mathrm{A}$
For ${\mathrm{V}}_0=16\mathrm{ }\mathrm{V}$

$16\mathrm{ }V-1000{\mathrm{ }\mathrm{i}}_0=6\mathrm{ }V$
${\mathrm{i}}_0=10\mathrm{ }\mathrm{m}\mathrm{A}$
${\mathrm{i}}_0-{\mathrm{i}}_2=\frac{6}{4000}=1.5\mathrm{ }\mathrm{m}\mathrm{A}$
${\mathrm{i}}_2=8.5\mathrm{ }\mathrm{m}\mathrm{A}$

Asked in: JEE Main 2019 (10 Apr Shift 2)

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