Question

A 5.0 V stabilized power supply is required to be designed using a 12 V DC power supply as input source. The maximum power rating of zener diode is 2.0 W. The minimum value of resistance $R_s$ in $\Omega$ connected in series with zener diode will be

• A. 16.5
• B. 17.5
• C. 18.5
• D. 15.5

Hint:

Logic Tip: The phrase "minimum value of resistance" always corresponds to the "maximum current" scenario. If the resistance were any lower than $17.5\text{ }\Omega$, the current would exceed $0.4\text{ A}$, dissipating more than $2.0\text{ W}$ and destroying the Zener diode!

Answer 1

The Correct Option is B

Concept:
In a Zener diode voltage regulator circuit, a series resistor ($R_s$) is placed between the unregulated input voltage ($V_{in}$) and the Zener diode to limit the current. To protect the Zener diode from burning out, the current passing through it must not exceed its maximum rated current ($I_{z(max)}$).
Step 1: Calculate the maximum allowed Zener current ($I_{z(max)}$).
The maximum power dissipation ($P_{max}$) of the Zener diode is given as $2.0\text{ W}$, and its Zener voltage ($V_z$) is $5.0\text{ V}$. Using the power formula $P = V \times I$: $$I_{z(max)} = \frac{P_{max{V_z}$$ $$I_{z(max)} = \frac{2.0}{5.0} = 0.4\text{ A}$$ This is the absolute maximum current the Zener diode can handle safely when no load is connected.
Step 2: Determine the voltage drop across the series resistor ($R_s$).
The input voltage $V_{in} = 12\text{ V}$ and the Zener maintains $V_z = 5.0\text{ V}$ across itself. The voltage drop across the series resistor is: $$V_{R_s} = V_{in} - V_z$$ $$V_{R_s} = 12 - 5.0 = 7.0\text{ V}$$
Step 3: Calculate the minimum required series resistance ($R_{s(min)}$).
To ensure the current never exceeds $0.4\text{ A}$, we use Ohm's law ($V = IR$) to find the minimum resistance required. This worst-case scenario assumes no load is connected, meaning all current flows through the Zener diode. $$R_{s(min)} = \frac{V_{R_s{I_{z(max)$$ $$R_{s(min)} = \frac{7.0}{0.4} = \frac{70}{4} = 17.5\text{ }\Omega$$