The current voltage relation of the diode is given by I = e(1000V/T-1) mA, where the applied voltage V is in volt and the temperature T is in kelvin. If a student makes an error measuring ± 0.01V while measuring the current of 5mA at 300K, what will be the error in the value of current in mA?

0.2 mA

0.02 mA

05 mA

0.05 mA

Solution

0.2 mA

Given, I =(e^1000V/T-1)mA
dv =±0.01 V
T = 300 K
I = 5 mA
I = e1^000V/T-1
I +1 = e^1000V/T
Taking log on both sides, we get
log(l+T) = 1000V/T
On differentiating,
$fraction numerator dl over denominator 1 plus 1 end fraction space equals space 1000 over straight T space dV dl space equals space fraction numerator 1000 over denominator straight l plus straight T end fraction space equals space 1000 over straight T space dV dl space equals space 1000 over straight T space straight x space left parenthesis straight l plus 1 right parenthesis space dV rightwards double arrow space dl space equals space 1000 over 300 space straight x space left parenthesis 5 plus 1 right parenthesis space straight x 0.01 space equals space 0.2 space mA$
So, error in the value of current is 0.2 mA

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