For Zener diode regulator design, always calculate the resistor value based on the maximum input voltage to ensure the Zener diode doesn’t exceed its power rating. Neglecting load current provides a safety margin
The total current is given by:
\[ I_t = \frac{P_t}{V_t} \]
Substitute the given values:
\[ I_t = \frac{1.6}{8} = 0.2 \, \text{A} \]
The voltage drop across \( R_s \) is:
\[ \Delta V = 10 - 8 = 2 \, \text{V} \]
Using Ohm’s Law:
\[ R_s = \frac{\Delta V}{I_t} \]
Substitute the values:
\[ R_s = \frac{2}{0.2} \]
\[ R_s = 10 \, \Omega \]
The series resistance (\( R_s \)) is 10 Ω.
The output of the given circuit is
Let $ P_n = \alpha^n + \beta^n $, $ n \in \mathbb{N} $. If $ P_{10} = 123,\ P_9 = 76,\ P_8 = 47 $ and $ P_1 = 1 $, then the quadratic equation having roots $ \alpha $ and $ \frac{1}{\beta} $ is: