Question

The diode used in the circuit indicated as the diagram has a constant voltage drop of $0.5V$ at all currents and a maximum power rating of $100mW$. Calculate the value of the resistor $R$, connected in series with the diode in order to obtain the maximum current?

$\begin{align}
  & A.1.5\Omega \\
 & B.5\Omega \\
 & C.6.67\Omega \\
 & D.200\Omega \\
\end{align}$

Answer 1

Hint: The current through the circuit has to be found first. For that the maximum power rating is to be divided with the voltage drop occurring. Then we have to find the voltage drop across the resistance. Finally find the value of the resistance by taking the ratio of the voltage drop across the resistance to the current in the circuit.

Complete answer:
It has been mentioned in the question that,
Voltage drop in the circuit is given as,
${{V}_{drop}}=0.5V$
Maximum power rating can be written as,
$P=100mW$
First of all we have to find the current in the circuit. For that the maximum power rating is to be divided with the voltage drop in the circuit. Therefore we can write that,
$i=\dfrac{P}{{{V}_{drop}}}$
Substituting the values in it will give,
$i=\dfrac{100\times {{10}^{-3}}}{0.5}=0.2A$
Now we have to find the voltage drop across the resistance. It can be found by taking the difference of the voltage supplied and the voltage drop occurring due to diode. From the figure we can see that the voltage supplied is given as,
$V=1.5V$
So the voltage drop across the resistance will be found using the relation,
${{V}_{r}}=V-{{V}_{drop}}$
Substituting the values in it will give,
${{V}_{r}}=1.5-0.5=1V$
As the resistor is connected in series in the circuit, the current will be the same.
Therefore we can write that the value of resistance will be,
$R=\dfrac{{{V}_{r}}}{i}$
Substituting the values in it will give,
$R=\dfrac{1}{0.2}=5\Omega $

So, the correct answer is “Option B”.

Note:
The current is the flow of charge taking place in a period of time. The power of the circuit is given by the work done or the heat produced per unit time. The unit of the power is given as watt. The resistance of a material is directly proportional to the length of the material and inversely proportional to the area of the material.