The nominal Zener voltage (Vz0) of a Zener diode is the voltage across the diode when it is reverse-biased at its specified test current. For the 9.1V Zener diode, at a test current of 20 mA, we can state that:
Vz0 = 9.1V
This is given directly in the problem. Now, to find the Zener voltage at different currents, we need to consider the incremental resistance specified, which is 10 ohms.
To find the Zener voltage at 10 mA:
1. Calculate the change in current from the test current:
ΔI = 20 mA – 10 mA = 10 mA = 0.010 A
2. Calculate the voltage drop across the incremental resistance:
ΔV = R imes ΔI = 10 ext{ ohms} imes 0.010 ext{ A} = 0.1 ext{ V}
3. Since the Zener voltage decreases for a current less than the test current, we can subtract this drop from Vz0:
Vz(10 mA) = Vz0 – ΔV = 9.1 ext{ V} – 0.1 ext{ V} = 9.0 ext{ V}
Next, we find the Zener voltage at 50 mA:
1. Calculate the change in current:
ΔI = 50 mA – 20 mA = 30 mA = 0.030 A
2. Calculate the voltage drop across the incremental resistance:
ΔV = R imes ΔI = 10 ext{ ohms} imes 0.030 ext{ A} = 0.3 ext{ V}
3. Since the Zener voltage increases for a current greater than the test current, we add this drop to Vz0:
Vz(50 mA) = Vz0 + ΔV = 9.1 ext{ V} + 0.3 ext{ V} = 9.4 ext{ V}
In summary:
- Vz0 = 9.1 V
- Vz(10 mA) = 9.0 V
- Vz(50 mA) = 9.4 V