Question

The circuit shown in the figure. Determine the current through Zener diode. (Given: Zener diode break down. Voltage ${\mathrm{V}}_z=5.6\mathrm{V}$).

• A. $7mA$
• B. $17mA$
• C. $10mA$
• D. $15mA$

Answer 1

The correct option is C

$10mA$

Step 1: Draw the required figure

Zener diode break down the voltage

${\mathrm{V}}_z=5.6\mathrm{V}$

The resistors are,

$$\begin{gathered} R_1=200 \\ {\mathrm{R}}_2=800 \end{gathered}$$

Step 2: Formula used

Ohm's law-

$V=IR$

where, $V,I,R$ are voltage current and resistance respectively.

Step 3: Calculating the current across an $800\Omega$ resistor

From ohm's law-

A Zener breakdown potential difference across an $800\Omega$ resistor is ${\mathrm{V}}_z=5.6\mathrm{V}$

$\Rightarrow I_{\mathit{2}}=\frac{V_{\mathit{z}}}{R_{\mathit{2}}}$

$I_2$ is the current across $800\Omega$

Now substitute the values ${\mathrm{V}}_{\mathrm{z}},{\mathrm{R}}_2$

$$\begin{gathered} \Rightarrow I_{\mathit{2}}=\frac{5.6}{800} \\ \Rightarrow I_{\mathit{2}}=7\mathrm{mA} \end{gathered}$$

Step 4: Calculating the voltage across $200$Ohm

The voltage across the resistor is -

$$\begin{gathered} ∆\mathrm{V}=\mathrm{V}-{\mathrm{V}}_{\mathrm{z}} \\ ∆\mathrm{V}=9-5.6 \\ ∆\mathrm{V}=3.4\mathrm{V} \end{gathered}$$

Step 5:Calculating the current across an $200\Omega$ resistor

The current across a resistor

$$\begin{gathered} \Rightarrow I_{\mathit{1}}=\frac{\mathit{∆}V}{R_1} \\ \Rightarrow I_{\mathit{1}}=\frac{3.4}{200} \\ \Rightarrow I_{\mathit{1}}=17\mathrm{mA} \end{gathered}$$

Step 3: Calculate the current through the Zener diode

Note that the current through Zener diode,

from the figure, it is clear that-

$I_1=I_Z+I_2$

$$\begin{gathered} \Rightarrow I_Z\mathit{=}{I}_{\mathit{1}}\mathit{-}{I}_2 \\ \Rightarrow I_Z\mathit{=}\mathit{17}mA\mathit{-}\mathit{7}\mathrm{mA} \\ \Rightarrow I_Z\mathit{=}\mathit{10}mA \end{gathered}$$

Therefore the current through Zener diode,$I_Z=10mA$.

Hence, option C is the correct answer.