Question
Question: The current voltage relation of diode is defined by \(I=\left( {{e}^{\dfrac{1000V}{T}}}-1 \right)\)....
The current voltage relation of diode is defined by I=eT1000V−1. 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 ±0.01V while measuring the current of 5mA at 300K, what can be the error in the value of current in mA?
A.0.5mAB.0.05mAC.0.2mAD.0.02mA
Solution
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=eT1000V−1
The value of the current is mentioned in the question as,
I=5A
Substituting the value of current in it will give,
5=eT1000V−1
Rearranging this equation will give,
eT1000V=6………….. (1)
Again let us write the same equation,
I=eT1000V−1
Let us differentiate the whole equation with respect to volume. This can be written as,
dVdI=eT1000V×T1000
Rearranging the equation will give,
dI=eT1000V×T1000dV
Substitute the equation (1) in this equation,
dI=6×T1000×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=±0.01V
Substituting these all in the equation will give,