Question

The equation $I=\left[e^{\left(\right. \pi \times 100 \times V \left.\right) / T} - 1\right]mA$ relates current and voltage in case of a diode where the applied $V$ is in volts and the temperature $T$ is in kelvin. If an error of $\pm0.01V$ is made in measuring the voltage while measuring a current of $24mA$ at $157K$ , calculate the error in the value of current (in $μA$ ). (Take $\pi =3.14$ )

Answer 1

$I=\left[e^{\left(\right. \pi \times 100 \times V \left.\right) / T} - 1\right]mA$
When $I=24mA,e^{\left(\right. \pi \times 100 \times V \left.\right) / T}=25mA$
Also, $dI=\left[e^{\left(\right. \pi \times 100 \times V \left.\right) / T}\right]\times \left(\frac{\pi \times 100}{T}\right)dV$
$=25\times \frac{3 . 14 \times 100}{157}\times \left(\right.0.01\left.\right)$
$=25\times \frac{100}{50}\times \left(\right.0.01\left.\right)$
$\therefore dI=0.5mA=500μA$