Calculate Total Current \( I_S \):
The total resistance in the circuit is \( 200\Omega + 500\Omega = 700\Omega \). The source voltage is 20V, so the total current \( I_S \) flowing through the series resistance is:
\[ I_S = \frac{20}{700} = \frac{20}{700} \approx 28.6 \text{ mA} \]
Determine Voltage Across the 500 \( \Omega \) Resistor and Zener Diode:
Since the Zener diode is in breakdown mode (10V across it), the voltage drop across the 500 \( \Omega \) resistor is also 10V. The current \( I_1 \) through the 500 \( \Omega \) resistor is:
\[ I_1 = \frac{10}{500} = 20 \text{ mA} \]
Calculate Current Through the Zener Diode \( I_Z \):
The current \( I_Z \) through the Zener diode is:
\[ I_Z = I_S - I_1 = 28.6 - 20 \approx 30 \text{ mA} \]
A pure silicon crystal with 5 × 1028 atoms m−3 has ni = 1.5 × 1016 m−3. It is doped with a concentration of 1 in 105 pentavalent atoms, the number density of holes (per m3) in the doped semiconductor will be:
Let \( y = f(x) \) be the solution of the differential equation
\[ \frac{dy}{dx} + 3y \tan^2 x + 3y = \sec^2 x \]
such that \( f(0) = \frac{e^3}{3} + 1 \), then \( f\left( \frac{\pi}{4} \right) \) is equal to:
Find the IUPAC name of the compound.
If \( \lim_{x \to 0} \left( \frac{\tan x}{x} \right)^{\frac{1}{x^2}} = p \), then \( 96 \ln p \) is: 32