GATE 2022 IN Q.31: solution and answer

GATE 2022 · INQ.31 · 1 mark · NAT

A Zener diode is used as a 4 V voltage regulator in the circuit shown. Given that the diode requires a minimum current of 4 mA for voltage regulation, the maximum current (in milliamperes) permitted to flow through the load $R_{L}$ is ________ (round off to one decimal place)

GATE 2022 IN question 31: A 16 V DC voltage source on the left, positive terminal at the top. — Figure from the GATE 2022 IN paper. It is part of the question.

Answer and solution

ANSWER

The maximum permitted load current is 6.0 mA.

Official answer: 6.0Source: Official answer key, GATE 2022 IN (IIT Kharagpur)

While the Zener is regulating, it holds the load node at $V_{Z} = 4 V$ . The voltage across the series resistor is therefore fixed at $16 - 4 = 12 V$ .
Ohm's law on the series resistor gives a source current that does not depend on the load: $I_{S} = \frac{16 - 4}{1200} = \frac{12}{1200} A = 10 mA$
KCL at the Zener–load node: $I_{S} = I_{Z} + I_{L}$ . Every milliampere the load draws is taken from the Zener current.
Regulation needs $I_{Z} \geq I_{Z, m i n} = 4 mA$ , so the load current is largest when the Zener carries exactly its minimum: $I_{L, m a x} = I_{S} - I_{Z, m i n} = 10 - 4 = 6 mA$
Check: this corresponds to $R_{L, m i n} = \frac{4 V}{6 mA} \approx 667 Ω$ . A smaller $R_{L}$ would draw more than 6 mA, the Zener current would fall below 4 mA and the diode would stop regulating. Answer: $6.0 mA$ .

KEY IDEA

In a shunt Zener regulator, the Zener fixes the output voltage, so the current through the series resistor is fixed at $(V_{S} - V_{Z}) / R_{S}$ . The load and the Zener share that current. The load can take everything except the minimum current the Zener needs to stay in breakdown: $I_{L, m a x} = I_{S} - I_{Z, m i n}$ .

WATCH OUT FOR

Computing $I_{S} = 16/1200 \approx 13.3 mA$ from the full source voltage instead of the 12 V actually across the resistor. Another error is adding $I_{Z, m i n}$ to the source current instead of subtracting it (14 mA). A third is answering the source current (10 mA) without taking out the Zener's minimum 4 mA.

From the GATE 2022 IN paper. Every question of this paper · Download the full paper · All 25 Diode circuits questions, with notes

GATE 2022 IN Q.31: solution and answer

Answer and solution

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