Question

The current-voltage relation of the diode is given by $I=(e^{1000V/T}–1)mA$, where the applied $V$ is in volts and the temperature $T$ is in degree Kelvin. If a student makes an error measuring ±$0.01V$ while measuring the current of $5mAat300K$, what will be the error in the value of current in $mA$

• A. $0.2mA$
• B. $0.02mA$
• C. $0.5mA$
• D. $0.05mA$

Answer 1

The correct option is A

$0.2mA$

Step 1: Given data:

The current-voltage relation of the diode $I=(e^{1000V/T}–1)mA$

Where applied $V$ is in volts and temperature $T$ is in degrees Kelvin.

A measuring error of $dV=\pm 0.01V$

The current $I=5mA$

The temperature, $T=300k$

Step 2: Calculating the error in the value of the current

The current-voltage relation of the diode-

$I=(e^{1000V/T}–1)mA$…………………………….(1)

putting the values of all known quantities-

$I=5mA$………………(2)

equating equations 1 and 2-

$$\begin{gathered} 5=(e^{1000V/T}–1) \\ {e}^{1000V/T}=6 \end{gathered}$$

Using the given equation,

$$\begin{gathered} I=(e^{1000V/T}–1) \\ ondifferentiating, \\ \frac{dI}{dV}=\frac{d\left((e^{1000V/T}–1)\right)}{dv} \\ dI=e^{1000V/T}\times \left(1000/T\right)dV \\ dI=6\times \frac{1000}{300}\times \left(0.01\right) \\ dI=0.2mA \end{gathered}$$

Therefore the error in the value of the current is $0.2mA$.

Hence, option A is the correct answer.