Question 71 of 209

In a given circuit diagram, a $5V$ zener diode along with a series resistance is connected across a $50V$ power supply. The minimum value of the resistance required, if the maximum zener current is $90mA$ will be $\text{Ω.}$

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Answer: 500

Voltage across, ${R}_{L}=5V$
$\Rightarrow {i}_{2}=\dfrac{5}{{R}_{L}}$
Also, voltage across $R=50-5=45$ volt
$v=iR\Rightarrow R=\dfrac{v}{i}=\dfrac{45}{{i}_{i}+{i}_{2}}$
$R=\dfrac{45}{90mA+\dfrac{5}{{R}_{L}}}$
Current in zener diode is maximum when ${R}_{L}\rightarrow \infty$
$\left({i}_{2}\rightarrow 0\right.$ and $\left.{i}_{i}=i\right)$
So $R=\dfrac{45}{90mA}=500\Omega$