Question
The current voltage relation of a diode is given by $$I = \left( {{e^{1000V/T}} - 1} \right)mA,$$ where the applied voltage $$V$$ is in volts and the temperature $$T$$ is in degree kelvin. If a student makes an error measuring $$ \pm 0.01\,V$$ while measuring the current of $$5\,mA$$ at $$300\,K,$$ what will b the error in the value of current in $$mA$$ ?
A.
$$0.2\,mA$$
B.
$$0.02\,mA$$
C.
$$0.5\,mA$$
D.
$$0.05\,mA$$
Answer :
$$0.2\,mA$$
Solution :
The current voltage relation of diode is
$$I = \left( {{e^{1000V/T}} - 1} \right)mA\,\,\left( {{\text{given}}} \right)$$
When, $$I = 5\,mA,{e^{1000V/T}} = 6\,mA$$
Also, $$dI = \left( {{e^{1000V/T}}} \right) \times \frac{{1000}}{T}\,\,\left( {{\text{By}}\,{\text{exponential function}}} \right)$$
$$\eqalign{
& = \left( {6\,mA} \right) \times \frac{{1000}}{{300}} \times \left( {0.01} \right) \cr
& = 0.2\,mA \cr} $$