The current voltage relation of diode is given by $I = (e^{1000 V / T} - 1) m A$ , where the applied voltage V is in volts and the temperature $T$ is in degree Kelvin. If a student makes an error of $\pm 0.01 V$ while measuring the current of $5 m A$ at $300 K,$ what will be the error in the value of current in $m A$ ?

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$0.5 m A$

$0.2 m A$

$0.02 m A$

$0.05 m A$

answer is B.

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Detailed Solution

As, $I = (e^{1000 V / T} - 1) mA$ ….(i)

Here, $I = 5 mA$ at $T = 300 K$

$d V = 0.01 V, ∴ 5 = (e^{1000 V / T} - 1) \Rightarrow e (1000 V / T) = 6 mA$

Differentiating eqn. (i), we get $d I = (\frac{1000}{T}) e^{(1000 V / T)} d V$

$d I = \frac{1000}{300} (6) (0.01) = 0.2 mA$

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