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P-N Junction Diode question from JEE Main 2014

Q103JEE Main 2014Difficult

P-N Junction Diode

The current voltage relation of diode is given by $I = \left(e^{1000V/T} - 1\right)\text{ mA},$ 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 be the error in the value of current in $mA$ ?

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Answer: (a)

Differentiate: $\frac{dI}{dV} = \frac{1000}{T} e^{1000V/T} = \frac{1000}{T}(I + 1)$ mA/V.
At $I = 5$ mA and $T = 300$ K: $\frac{dI}{dV} = \frac{1000}{300} \times 6 = 20$ mA/V.
$\Delta I = 20 \times 0.01 = 0.2$ mA.
So the answer is (a) $0.2$ mA.

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