A Zener diode has a breakdown voltage of Vz = 7 V at 300 K, with a temperature coefficient of 2.3 mV/°C. What is the new breakdown voltage Vz at 400 K?

Explanation:

A Zener diode has a breakdown voltage of Vz = 7 V at 300 K, with a temperature coefficient of 2.3 mV/°C. To find the new breakdown voltage Vz at 400 K, we need to consider the change in temperature and how it affects the breakdown voltage.

Calculation:

1. First, determine the temperature difference:

• The initial temperature (T1) = 300 K
• The final temperature (T2) = 400 K
• Temperature difference (ΔT) = T₂ - T₁ = 400 K - 300 K = 100 K

2. Convert the temperature difference from Kelvin to Celsius:

• Since the temperature coefficient is given in mV/°C, we need to use the equivalent Celsius temperature difference.
• Note: The temperature change is the same in Celsius and Kelvin, so ΔT = 100 °C.

3. Calculate the change in breakdown voltage using the temperature coefficient:

• Temperature coefficient = 2.3 mV/°C
• Change in breakdown voltage (ΔVz) = Temperature coefficient × Temperature difference
• ΔVz = 2.3 mV/°C × 100 °C = 230 mV

4. Convert the change in breakdown voltage to volts:

• ΔVz = 230 mV = 0.230 V

5. Determine the new breakdown voltage:

• Initial breakdown voltage (Vz) = 7 V
• New breakdown voltage (Vz_new) = Initial breakdown voltage + Change in breakdown voltage
• Vz_new = 7 V + 0.230 V = 7.23 V

Conclusion:

The new breakdown voltage at 400 K is 7.23 V, which corresponds to Option 2.