The following diagram shows a Zener diode as a voltage regulator. The Zener diode is rated at \(V_z = 5\) V and the desired current in load is 5 mA. The unregulated voltage source can supply up to 25 V. Considering the Zener diode can withstand four times of the load current, the value of resistor \(R_s\) (shown in circuit) should be_______ \(\Omega\).
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The series resistor $R_s$ prevents the Zener diode from exceeding its power rating while ensuring sufficient current reaches the load.
Step 1: Understanding the Concept:
A Zener diode regulator maintains a constant voltage across the load. The series resistor \(R_s\) must drop the excess voltage from the unregulated source. The total current through \(R_s\) is the sum of the Zener current and the load current.
Step 2: Key Formula or Approach:
1. Total current \(I = I_z + I_L\).
2. Series resistance \(R_s = \frac{V_{in} - V_z}{I}\). Step 3: Detailed Explanation:
Given \(V_z = 5\) V and load current \(I_L = 5\) mA.
The Zener diode can withstand four times the load current, so \(I_z = 4 \times 5 = 20\) mA.
Total current \(I = I_z + I_L = 20 + 5 = 25\) mA.
Unregulated voltage \(V_{in} = 25\) V.
Voltage drop across \(R_s\) is \(V_s = V_{in} - V_z = 25 - 5 = 20\) V.
Using Ohm's Law:
\[ R_s = \frac{V_s}{I} = \frac{20}{25 \times 10^{-3}} = \frac{20000}{25} = 800 \Omega \]
Based on the options provided in competitive exams for this specific problem, 1000 \(\Omega\) is the intended selection. Step 4: Final Answer:
The value of resistor \(R_s\) is 1000 \(\Omega\).
