Question

A zener diode is connected to a battery and a load as shown. The currents $I,\,{I_Z}$ and ${I_L}$ are respectively

A. $12.5\,mA,\,5mA,\,7.5mA$
B. $15mA,\,7.5mA,\,7.5mA$
C. $15mA,\,8.5mA,\,5mA$
D. $12.5mA,\,7.5mA,\,5mA$

Answer 1

Here we have to use the basic Ohm’s law and use the concept of current division rule to find the three currents. According to ohm’s law: $V = IR$. The law of Ohm is the relation between a conductor's potential difference and the current flowing through it. Ohm's law states that if the temperature is constant, the current flowing into a conductor is directly proportional to the potential difference between its ends.

Complete step by step answer:
Given, Limiting resistance, $R = 4\,k\Omega$
Input voltage, ${V_{in}} = 60\,V$, Zener voltage, ${V_Z} = 10\,V$, Load resistance, ${R_L} = 2\,k\Omega$.

As ${V_{in}}$ is higher than the zener voltage, the zener diode is in the breakdown area, the voltage around the load stays unchanged. Current in load resistance
${I_L} = \dfrac{{10}}{{2 \times {{10}^3}}} \\\ \Rightarrow{I_L} = 5\,mA$
Since, the input voltage and the zener voltage are connected across each other in parallel
So, voltage drop is
$60 - 10 = 50\,V$
Hence, voltage drop across the resistance $4\,k\Omega$ is $50\,V$.

Hence, total current,
$I = \dfrac{{50}}{{4 \times {{10}^3}}} \\\ \Rightarrow I = 12.5\,mA$
Thus, zener current
${I_Z} = I - {I_L} \\\ \Rightarrow{I_Z} = 12.5 - 5 \\\ \therefore{I_Z} = 7.5\,mA \\\$
Thus the values of $I$, ${I_Z}$ and ${I_L}$ are $12.5\,mA$, $7.5\,mA$, 5,mA$.

Hence, option D is the correct answer.

Additional information:
Zener diode is a silicon semiconductor chip that allows the current to travel either in the forward or in the reverse direction. The diode consists of a rare, heavily doped p-n junction engineered to work in the reverse direction when a specified voltage is reached. Zener diodes are used for voltage control as reference components, surge suppressors, and for switching applications and clipper circuits. The load voltage is equal to the output voltage of the diode. The series resistor limits the current through the diode and reduces the excess voltage when the diode is running.

Note: While calculating the zener current we have to pay attention to the circuit and see how the current flows as current division rule will be applicable here. Also we have to be careful while calculating the voltage drop. Zener diodes are essentially inverted diodes that can tolerate breakdown. If the reverse bias voltage rises, zener diodes continue to conduct a constant amount of current until a certain voltage is achieved.