The 6 V zener diode shown in figure has zero zener resistance and a knee current of 5 mA. The minimum value of R so that the voltage across it does not fall below 6 V is :
80 Ω
The zener regulates only while it keeps conducting, so the whole problem is a current-budget question.
Step 1 — the series current is fixed. With the zener holding its terminals at 6 V, the drop across the 50 Ω resistor is the same whatever the load does:
\(I_{S}=\dfrac{V_{in}-V_{Z}}{R_{S}}=\dfrac{10-6}{50}=\dfrac{4}{50}=80\ \text{mA}\)
This 80 mA is the total current available, and it must divide between the zener and the load:
\(I_{S}=I_{Z}+I_{L}\)
Step 2 — the zener must keep at least its knee current. Below the knee (5 mA) the device leaves the breakdown region and stops holding 6 V. So
\(I_{L(max)}=I_{S}-I_{Z(min)}=80-5=75\ \text{mA}\)
Step 3 — convert the maximum load current into the minimum load resistance. A smaller R draws a larger current, so the current limit sets a lower bound on R:
\(R_{min}=\dfrac{V_{Z}}{I_{L(max)}}=\dfrac{6}{75\ \text{mA}}=80\ \Omega\)
which is option 2.
| R | IL | IZ = 80 − IL | Regulating? |
|---|---|---|---|
| 1.2 kΩ | 5 mA | 75 mA | Yes, comfortably |
| 80 Ω | 75 mA | 5 mA | Just at the knee |
| 50 Ω | 120 mA | Impossible | No — zener drops out |
What happens if R is made smaller than 80 Ω. The load now wants more than 80 mA, but only 80 mA can flow through the 50 Ω resistor while the output sits at 6 V. The output voltage must therefore fall, the zener stops conducting altogether, and the circuit degenerates into a plain potential divider — regulation is lost. That is exactly the condition the question asks us to avoid.
The complementary design check is the zener's power rating at the other extreme. With the load removed entirely the zener carries the whole 80 mA and dissipates
\(P_{Z}=V_{Z}I_{Z}=6\times0.08=0.48\ \text{W}\)
so a half-watt device would be marginal. A practical shunt regulator has to satisfy both limits at once: enough current to stay above the knee at maximum load, and not so much that the zener overheats at minimum load.
Hence, the minimum value of R is 80 Ω.
Similar Questions
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B. Junction capacitance varies with time
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