Question

The current voltage relation of diode is defined by $I=\left( {{e}^{\dfrac{1000V}{T}}}-1 \right)$. In this equation, the applied voltage $V$ is in volts and the temperature $T$ is in degree Kelvin. If a student makes an error measuring $\pm 0.01V$ while measuring the current of $5mA$ at $300K$, what can be the error in the value of current in $mA$?
$\begin{align}
  & A.0.5mA \\
 & B.0.05mA \\
 & C.0.2mA \\
 & D.0.02mA \\
\end{align}$

Answer 1

Hint: First of all, substitute the value of current in the general equation of current given in the question and simplify the equation. Differentiate the same equation with respect to volume and substitute the values of temperature and error in volume measurement. These will help you in solving this question.

Complete step by step solution:
The given equation of the current in question can be written as,
$I=\left( {{e}^{\dfrac{1000V}{T}}}-1 \right)$
The value of the current is mentioned in the question as,
\[I=5A\]
Substituting the value of current in it will give,
$5=\left( {{e}^{\dfrac{1000V}{T}}}-1 \right)$
Rearranging this equation will give,
\[\left( {{e}^{\dfrac{1000V}{T}}} \right)=6\]………….. (1)
Again let us write the same equation,
$I=\left( {{e}^{\dfrac{1000V}{T}}}-1 \right)$
Let us differentiate the whole equation with respect to volume. This can be written as,
\[\dfrac{dI}{dV}={{e}^{\dfrac{1000V}{T}}}\times \dfrac{1000}{T}\]
Rearranging the equation will give,
\[dI={{e}^{\dfrac{1000V}{T}}}\times \dfrac{1000}{T}dV\]
Substitute the equation (1) in this equation,
\[dI=6\times \dfrac{1000}{T}\times dV\]
As it is mentioned in the question, the value of temperature is given as,
\[T=300K\]
The change in volume has been mentioned as,
\[dV=\pm 0.01V\]
Substituting these all in the equation will give,
\[\begin{align}
  & dI=6\times \dfrac{1000}{300}\times 0.01 \\
 & \Rightarrow dI=0.2mA \\
\end{align}\]
There the error in the value of current has been obtained.

The answer for this question is option C.

Note:
A diode is defined as a semiconductor equipment that specifically acts as a one-way switch for the current. It permits the current to flow only in one direction. And also it completely prevents the current from flowing in the opposite direction. Earlier days, the diodes were helpful in converting AC to DC and also to filter out the signal in radios. Nowadays the diodes are commonly used to protect electronics, send remote-control signals and even to light our homes.