Question

The equation $I=\left[e^{(\pi \times 100\times V)/T}-1\right]mA$ 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 $\pm 0.01V$ is made in measuring the voltage while measuring a current of $24mA$ at $157K$ , calculate the error in the value of current (in $\mu A$ ). (Take $\pi =3.14$ )

Answer 1

Answer: 500

$I=\left[e^{(\pi \times 100\times V)/T}-1\right]mA$
When $I=24mA,e^{(\pi \times 100\times V)/T}=25mA$
Also, $dI=\left[e^{(\pi \times 100\times V)/T}\right]\times \left(\frac{\pi \times 100}{T}\right)dV$
$=25\times \frac{3.14\times 100}{157}\times (0.01)$
$=25\times \frac{100}{50}\times (0.01)$
$\therefore dI=0.5mA=500\mu A$