Question

In the circuit shown, find the current through the Zener diode.

• A. $5\mathrm{mA}$
• B. $1\mathrm{mA}$
• C. $15\mathrm{mA}$
• D. $25\mathrm{mA}$

Answer 1

The correct option is D

$25\mathrm{mA}$

Step 1: Given data

From the diagram:

The value of resistance is ${\mathrm{R}}_1=1000\mathrm{ohm}$ and ${\mathrm{R}}_3=2000\mathrm{ohm}$

Let $R_2$ be the resistance across Zener diode.

Voltage across the battery is $\left(\mathrm{V}\right)=100\mathrm{volt}$

Voltage across the Zener diode is $\left({\mathrm{V}}_2\right)=50\mathrm{volt}$

Step 2: Apply Ohms Law

$\Rightarrow \mathrm{V}=\mathrm{I}\times \mathrm{R}$

Where, $V=$voltage, $I=$current, $R=$resistance

Step 3: Calculate the current passing through as shown in the circuit across 2000 ohm

The Zener diode is parallel to $2000ohm$, thus, the voltage across the Zener diode and the resistance is the same.

Therefore, apply formula

$$\begin{gathered} \Rightarrow \mathrm{I}=\frac{\mathrm{V}}{\mathrm{R}} \\ \Rightarrow {\mathrm{i}}_3=\frac{50\mathrm{volt}}{2000\mathrm{ohm}} \end{gathered}$$

Convert, $volt/ohm$ to $mA$, we have to multiply by $1000$

$$\begin{gathered} \Rightarrow {\mathrm{i}}_3=\frac{50}{2000}\times 1000 \\ \Rightarrow {\mathrm{i}}_3=25mA \end{gathered}$$

Step 4: Calculate potential differences across $1000\mathrm{ohm}$ and the electric current

$$\begin{gathered} \Rightarrow {\mathrm{V}}_1=\mathrm{V}-{\mathrm{V}}_2 \\ \Rightarrow {\mathrm{V}}_1=100-50 \\ \Rightarrow {\mathrm{V}}_1=50\mathrm{volt} \end{gathered}$$

So, the electric current passing through it,

$\Rightarrow {\mathrm{i}}_1=\frac{50volt}{1000ohm}$

Convert, $volt/ohm$ to $mA$, We have to multiply by $1000$

$$\begin{gathered} \Rightarrow {\mathrm{i}}_1=\frac{50}{1000}\times 1000 \\ \Rightarrow {\mathrm{i}}_1=50\mathrm{mA} \end{gathered}$$

Step 5: Calculate the current through the Zener diode

$$\begin{gathered} \Rightarrow {\mathrm{i}}_2={\mathrm{i}}_1-{\mathrm{i}}_3 \\ \Rightarrow {\mathrm{i}}_2=50-25 \\ \Rightarrow {\mathrm{i}}_2=25\mathrm{mA} \end{gathered}$$

Hence, option $\left(\mathrm{D}\right)$ is correct.