Question

A $ 5 $ V Zener diode is used to regulate the voltage across the load resistor $ {R_L} $ and the input voltage varies in between $ 10 $ V to $ 15 $ V. The load current also varies from $ 5 $ mA to $ 50 $ mA. Find the value of series resistance R. Given, $ {I_z}(\min ) = 20mA $
(A) $ 70\Omega $
(B) $ 90.91\Omega $
(C) $ 142.86\Omega $
(D) $ 71.43\Omega $

Answer 1

Hint :Read the given data twice and then decide the applicable law to find the series resistance R. Also, we will here use the Kirchoff’s voltage law and simplify the equation for the required value.

Complete Step By Step Answer:
When the load resistance is maximum, the Zener current $ ({I_z}) $ would be minimum and the output voltage will also be minimum.
Ther $ {I_T} = {I_z}(\min ) + {I_L}(\max ) $ efore,
By applying the Kirchhoff's Voltage law which is the second law which deals with the conservation of energy around the closed-circuit path. It states that for the closed loop series path the algebraic sum of all the voltage around any closed loop in the circuit is equal to zero.
The above law can be expressed as –
 $ {V_{in}}(\min ) - {V_z} = {I_T}R = [{I_z}(\min ) + {I_L}(\max )]R $
Make required R the subject –
 $ R = \dfrac{{{V_{in}}(\min ) - {V_z}}}{{[{I_z}(\min ) + {I_L}(\max )]}} $
Place the given values in the above equation –
 $ R = \dfrac{{10 - 5}}{{[20 + 50] \times {{10}^{ - 3}}}} $
Simplify the above equation
 $ R = \dfrac{5}{{70 \times {{10}^{ - 3}}}} $
By using the law of inverse multiplication of the power and exponent –
 $ R = \dfrac{{5 \times {{10}^3}}}{{70}} $
Find the factors of the term in denominator-
 $ R = \dfrac{{5 \times {{10}^3}}}{{7 \times 10}} $
Common factors from the numerator and the denominator cancel each other.
 $ R = 71.43\Omega $
From the given multiple choices, the option D is the correct answer.

Note :
Know the difference between the current and the voltage law of Kirchoff. Also, be good in basic mathematical solutions and multiples for the efficient and accurate answer. Kirchoff’s current law deals with the charge entering and leaving the network. Zener current and load current both are different, remember it and place the values accordingly.