Question

In the given circuit diagram, $I_L = 5$ mA and the Zener voltage is $V_Z = 5$ V. If $i_z = 4 i_L$, find the value of $R_s$ (in $\Omega$).

Hint:

In Zener regulator problems, always apply current division: $I_s = I_L + I_Z$ and remember that the Zener voltage remains constant across the load.

Answer 1

Correct Answer: 800

Concept: For a Zener diode voltage regulator:
The Zener diode maintains a constant voltage $V_Z$ across the load
Source current splits as: $I_s = I_L + I_Z$
Ohm’s law is applied across the series resistance $R_s$
Step 1: Given data Load current: \[ I_L = 5\ \text{mA} \] Given: \[ i_z = 4 i_L \Rightarrow I_Z = 4 \times 5 = 20\ \text{mA} \]
Step 2: Calculate source current \[ I_s = I_L + I_Z = 5 + 20 = 25\ \text{mA} \]
Step 3: Voltage across series resistance Supply voltage: \[ V_s = 25\ \text{V} \] Zener voltage: \[ V_Z = 5\ \text{V} \] \[ V_{R_s} = V_s - V_Z = 25 - 5 = 20\ \text{V} \] Step 4: Find $R_s$ using Ohm’s law \[ R_s = \frac{V_{R_s}}{I_s} = \frac{20}{25 \times 10^{-3}} = 800\ \Omega \]
Step 5: Hence, \[ \boxed{R_s = 800\ \Omega} \]