In the circuit shown, a 5 V Zener diode is used to regulate the voltage across load R₀ . The input is an unregulated DC voltage with a minimum value of 6 V and a maximum value of 8 V. The value of Rs is 6 Ω . The Zener diode has a maximum rated power dissipation of 2.5 W. Assuming the Zener diode to be ideal, the minimum value of R₀ is ______ Ω .

The correct answer is 30.

To find the minimum value of load resistance $R_0$ that maintains voltage regulation, we analyze the conditions required to keep the Zener diode in its breakdown region.

1. Given Parameters:
- Zener voltage: $V_Z=5\text{V}$
- Minimum input voltage: $V_{\mathrm{in},\min }=6\text{V}$
- Maximum input voltage: $V_{\mathrm{in},\max }=8\text{V}$
- Series resistance: $R_s=6\text{Ω}$
- Maximum power dissipation: $P_{Z,\max }=2.5\text{W}$

2. Maximum Allowable Zener Current:
The maximum rated current for the Zener diode $I_{Z,\max }$ is determined from its maximum power dissipation rating:
$I_{Z,\max }=\frac{P_{Z,\max }}{V_Z}=\frac{2.5\text{W}}{5\text{V}}=0.5\text{A}$

3. Condition for Voltage Regulation:
For the Zener diode to successfully regulate the voltage across the load $R_0$ at $5\text{V}$, it must remain in the breakdown state. This requires the Zener diode current $I_Z$ to be greater than or equal to zero:
$I_Z\ge 0$

Using Kirchhoff's Current Law (KCL) at the node connecting the series resistor, Zener diode, and load resistance:
$I_s=I_Z+I_L\Rightarrow I_Z=I_s-I_L$

Substituting this into the breakdown condition:
$I_s-I_L\ge 0\Rightarrow I_L\le I_s$

4. Calculating the Minimum Load Resistance $R_0$:
The most critical condition to maintain breakdown occurs when the input voltage is at its minimum value, $V_{\mathrm{in},\min }=6\text{V}$, because this yields the minimum current through the series resistor:
$I_{s,\min }=\frac{V_{\mathrm{in},\min }-V_Z}{R_s}=\frac{6-5}{6}=\frac{1}{6}\text{A}$

To maintain regulation, the load current $I_L=\frac{V_Z}{R_0}$ must not exceed this value:
$I_L\le I_{s,\min }$

Substituting the known values:
$\frac{5}{R_0}\le \frac{1}{6}$

Solving for $R_0$:
$R_0\ge 5\times 6$
$R_0\ge 30\text{Ω}$

Therefore, the minimum value of $R_0$ required to keep the Zener diode in the breakdown region and maintain voltage regulation is 30 Ω.