Zener Diode: Regulator Numericals Solved on a Real Datasheet

A Zener diode is a diode built to work safely in reverse breakdown, where the voltage across it stays close to a set value, the Zener voltage (Vz). You connect it reverse-biased: the banded end (cathode) towards the positive supply, in parallel with the load, with a resistor in series between the supply and that junction.

In forward bias it behaves like an ordinary diode. Its datasheet, the manufacturer's document of guaranteed limits, caps the forward voltage of the Vishay BZX55 series at 1.5 V at 200 mA (Vishay BZX55 datasheet, Rev. 2.0, 7 November 2024).

There are two breakdown mechanisms. As a rule of thumb, below around 5 V the Zener effect (carriers tunnelling through a very thin junction) dominates. Above that, avalanche breakdown (carriers knocking more carriers loose) takes over. The changeover is visible in the datasheet's temperature coefficient, which is negative for the 3.3 V part and positive from 6.2 V upwards (table below). For the junction itself, see our PN junction page.

Check breakdown, find I_L = Vz/R_L, find I_R = (Vin − Vz)/R, subtract to get I_Z = I_R − I_L, check the no-load power, then test both supply and load extremes. Each of the six steps below has a pass or fail test, so you can see where a circuit or an answer breaks. The setup is the shunt regulator (Zener in parallel with the load): supply Vin, series resistor R, then the Zener (Vz) and load (R_L) in parallel.

If a question says "find the current through the Zener", it is step 4. If it gives a power rating and asks for maximum current, it is Ptot/Vz. For the general habit of writing the circuit and the currents before touching numbers, see how to solve physics numericals.

With R = 100 Ω, a Vishay BZX55C5V1 on a supply of 8.1 V to 9.9 V (9 V ±10 %) and a load of 0 to 20 mA stays in breakdown at every extreme, but its current moves between 7 mA and 51 mA depending on where the true Vz falls. All figures below are our working from the datasheet's limits (Vz 4.8 V to 5.4 V, nominal 5.1 V).

Step 1 check: the smallest load resistance is 5.1 V ÷ 20 mA = 255 Ω. The breakdown threshold is 5.1 × (100 + 255)/255 ≈ 7.1 V, below the 8.1 V minimum supply, so it passes.

Worked line for the middle row: (8.1 − 5.1)/100 = 30 mA, minus 20 mA load = 10 mA. And (9.9 − 5.1)/100 = 48 mA, times 5.1 V = 245 mW.

What this shows:

• Resistor choice. The largest R that keeps 5 mA in the Zener at 8.1 V and full load is (8.1 − 5.1)/(20 + 5) mA = 120 Ω at nominal Vz. At the 5.4 V limit, 120 Ω leaves only 2.5 mA. So 100 Ω is the safer pick.
• Zener power. About 245 mW, just under half the 500 mW rating (49 %).
• Resistor power. The resistor dissipates between 202 mW and 260 mW at 9.9 V, depending on Vz, so a ½ W resistor is needed, not a ¼ W one.

Not constant: it moves by a fraction of a volt, because breakdown has a small resistance. In breakdown the curve is almost vertical but not perfectly, and the slope is the Zener's dynamic resistance (Zz), the change in voltage per change in current. The datasheet publishes maximum Zz values, shown below.

Source: Vishay BZX55 datasheet, Rev. 2.0, 7 November 2024. Zz is quoted at 5 mA and at the knee current of 1 mA (the low-current bend where breakdown starts). The temperature coefficient is in %/K (percent change per kelvin of temperature rise).

Using the 5V1 row, our worked estimates (ceilings, because they use the datasheet's maximum Zz):

• Supply wobble. ΔVout ≈ ΔVin × Zz/(R + Zz) = 35/135 ≈ 0.26 V for every 1 V change on the input.
• Load change. ΔVout ≈ ΔI_L × (R in parallel with Zz) = 20 mA × 25.9 Ω ≈ 0.52 V, about 10 % of 5.1 V. A load that swings from nothing to 20 mA can pull a "5.1 V" rail down by up to about half a volt.
• Low current. At 1 mA the resistance can be up to 550 Ω, about 16 times the 35 Ω at 5 mA (550 ÷ 35). Let I_Z fall to the knee and the "regulator" regulates poorly.
• Temperature. Over a 50 K rise, a 5V1 can drift by at most ±1 % (±0.05 V). A 12 V part can drift up to +5.5 % (0.66 V) at its maximum coefficient.

Our inference: if the load changes a lot, a part around 7.5 V to 8.2 V (7 Ω) regulates best. If temperature matters more, 5.1 V is the stable choice, since its coefficient straddles zero.

Four slips cause most wrong answers, and each has a quick test.

• Treating I_Z as I_L. The load current is Vz/R_L. The Zener current is what is left of the resistor current. If your I_Z equals Vz/R_L, you skipped step 4.
• Wiring the Zener in series with the load. The regulator is parallel. If your diagram has the Zener in line with the load, redraw it.
• Assuming the Zener always regulates. It only does so if Vin passes the step 1 test. A numerical with a very small R_L is often built so it fails.
• Checking power with the load on. The worst case is the load off. If your power answer uses I_R − I_L, redo it with I_R alone.

That document also sets no negative marking and lists "Semiconductors" under Std XI Physics (CET Cell syllabus).

So the six steps above are the whole numerical. Keep the formulas next to our HSC Physics formula sheet. For Central Board of Secondary Education (CBSE) students, the Physics (042) curriculum for Class XII 2026-27 does not mention Zener diodes (CBSE Physics curriculum).

The MHTCET 2027 Long Term Batch is taught by Rahul Jewaani (RG Sir) and costs ₹1,632 as of November 2026.

Padhna Aasaan Hai: try the routine above on paper first, and check your answers against the extremes in step 6.