Question

If voltage across Zener diode is 6V then find out the value of maximum resistance in this condition.
(a) $2\Omega $
(b) $1\Omega $
(c) $5\Omega $
(d) $4\Omega $

Answer 1

Hint: Zener diode is voltage regulator, it maintains constant voltage across a load. Zener diode is connected in parallel to the load.

Formula Used:
Ohm's law:
$I = \dfrac{V}{R}$ ……(1)
where,
I is current
V is voltage
R is resistance.
Effective resistance when 2 resistors are connected in series:
$R = {R_1} + {R_2}$ ……(2)

Step-by-step answer:

Given:
1. Zener voltage ${V_z} = 6V$
2. Current $I = 6mA$
3. Voltage supplied $V = 30V$
4. Load resistance is $1k\Omega $

To find: The resistance R in the given circuit.

Step 1 of 3:
Find the effective resistance in the circuit using eq (2):
${R_{eff}} = 1 + R$

Step 2 of 3:
Find current through the circuit using eq (1):
$
  I = \dfrac{{30}}{{{R_{eff}}}} \\
  I = \dfrac{{30}}{{1 + R}} \\
 $

Step 3 of 3:
Find voltage across load by using eq (1):
$V = IR$ ……(3)
Putting the value of I and R in eq (3):
$V = (\dfrac{{30}}{{1 + R}}).(1)$ ……(4)
This voltage is equal to Zener voltage as Zener diode maintains the voltage across the load. It is given that ${V_z} = 6V$. Equating this with eq (4):
$
  {V_z} = (\dfrac{{30}}{{1 + R}}) \\
  6 = (\dfrac{{30}}{{1 + R}}) \\
  R = 4k\Omega \\
 $

Correct Answer: The value of maximum resistance is (b) $1\Omega $.

Note: In questions like these observe the circuit diagram carefully and find out the given information. Voltage across Zener diodes will be the same as that calculated for the load resistance. Use Ohm’s law to find I, V and R.