In a given circuit diagram, a 5V zener diode along with a series...

Voltage across, ${R}_{L} = 5V$

$⇒ {i}_{2} = \dfrac{5}{{R}_{L}}$

Also, voltage across $R = 50 - 5 = 45$ volt

$v = iR ⇒ R = \dfrac{v}{i} = \dfrac{45}{{i}_{i} + {i}_{2}}$

$R = \dfrac{45}{90mA + \dfrac{5}{{R}_{L}}}$

Current in zener diode is maximum when ${R}_{L} \to \infty$
\left({i}_{2} \to 0\right)$and {i}_{i} = i)</p><p>So$R = $\dfrac{45}{90mA} =$500Ω