Calculating Zener Resistance

The Zener resistance ($R_z$) of a Zener diode is a measure of how much the Zener voltage changes with respect to a change in Zener current in the breakdown region. It is essentially the dynamic resistance of the diode operating in its reverse breakdown mode.

The formula for Zener resistance is given by the ratio of the change in Zener voltage ($\Delta V_z$) to the corresponding change in Zener current ($\Delta I_z$):

\[ R_z = \frac{\Delta V_z}{\Delta I_z} \]

In this question, we are given the following values:

• Change in Zener voltage, \(\Delta V_z = 50 \text{ mV}\)
• Change in Zener current, \(\Delta I_z = 2.5 \text{ mA}\)

First, we need to convert these values to standard units (Volts and Amperes):

• \(\Delta V_z = 50 \text{ mV} = 50 \times 10^{-3} \text{ V}\)
• \(\Delta I_z = 2.5 \text{ mA} = 2.5 \times 10^{-3} \text{ A}\)

Now, we can substitute these values into the formula for Zener resistance:

\[ R_z = \frac{50 \times 10^{-3} \text{ V}}{2.5 \times 10^{-3} \text{ A}} \]

We can cancel out the \(10^{-3}\) terms from the numerator and the denominator:

\[ R_z = \frac{50}{2.5} \text{ } \Omega \]

Performing the division:

\[ R_z = 20 \text{ } \Omega \]

Therefore, the Zener resistance of the diode is \(20 \text{ } \Omega\).