Question:
The current voltage relation of diode is given by $I=\left(e^{1000 V / T}-1\right) mA$, where the applied voltage $V$ is in volt and the temperature $T$ is in kelvin. If a student makes an error measuring $\pm 0.01\, V$ while measuring the current of
The current voltage relation of diode is given by $I=\left(e^{1000 V / T}-1\right) mA$, where the applied voltage $V$ is in volt and the temperature $T$ is in kelvin. If a student makes an error measuring $\pm 0.01\, V$ while measuring the current of
Updated On: Aug 21, 2024
- 0.2 m A
- 0.02 mA
- 0.5 mA
- 0.05 mA
Hide Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Given, I = $ ( e^{ 1000 V / T } - 1) $ mA, dV = $\pm 0.01$ V
T = 300 K
So, I = $ e^{ 1000 V /T } - 1 $
I + 1 = $ e^{ 1000 V / T} $
Taking log on both sides, we get log (I + 1) = $ \frac{1000 \, V}{ T} $
On differentiating. $ \frac{ dI}{ I + 1} = \frac{ 1000}{ T} $ dV
dI = $ \frac{ 1000}{ T} \times (I + 1) $ dV
$\Rightarrow dI = \frac{ 1000}{ 300} \times ( 5 + 1) \times 0.01 $ = 0 . 2 m A
So, error in the value of current is 0.2 mA.
T = 300 K
So, I = $ e^{ 1000 V /T } - 1 $
I + 1 = $ e^{ 1000 V / T} $
Taking log on both sides, we get log (I + 1) = $ \frac{1000 \, V}{ T} $
On differentiating. $ \frac{ dI}{ I + 1} = \frac{ 1000}{ T} $ dV
dI = $ \frac{ 1000}{ T} \times (I + 1) $ dV
$\Rightarrow dI = \frac{ 1000}{ 300} \times ( 5 + 1) \times 0.01 $ = 0 . 2 m A
So, error in the value of current is 0.2 mA.
Was this answer helpful?
0
0
Top Questions on Uncertainty in Measurement
If the uncertainty in velocity and position of a minute particle in space are, \(2.4 × 10^{–26}\) \((m s^{–1)}\) and \(10^{–7} (m)\), respectively. The mass of the particle in g is _____ . (Nearest integer)
(Given : \(h = 6.626 × 10^{–34} Js\))- JEE Main - 2022
- Chemistry
- Uncertainty in Measurement
- The density of a material in $CGS$ system of units is $4\,g\,cm^3$. In a system of units in which unit of length is $10\,cm$ and unit of mass is $100\,g$. the value of density of material will be
- NEET (UG) - 2011
- Chemistry
- Uncertainty in Measurement
- The magnitude of any physical quantity
- Punjab PMET - 2006
- Chemistry
- Uncertainty in Measurement
- Match the following prefixes with their multiples:
S.No Prefixes Multiples (i) micro 106 (ii) deca 109 (iii) mega 10–6 (iv) giga 10–15 (v) femto 10 - CBSE Class XI
- Chemistry
- Uncertainty in Measurement
- How many significant figures are present in the following?
(i) 0.0025
(ii) 208
(iii) 5005
(iv) 126,000
(v) 500.0
(vi) 2.0034- CBSE Class XI
- Chemistry
- Uncertainty in Measurement
View More Questions
Questions Asked in JEE Main exam
- The de-Broglie wavelength associated with a particle of mass \( m \) and energy \( E \) is \[\lambda = \frac{h}{\sqrt{2mE}}.\]The dimensional formula for Planck's constant is:
- JEE Main - 2024
- de broglie hypothesis
- If the foci of a hyperbola are the same as that of the ellipse \( \frac{x^2}{9} + \frac{y^2}{25} = 1 \) and the eccentricity of the hyperbola is \( \frac{15}{8} \) times the eccentricity of the ellipse,then the smaller focal distance of the point \( \left( \sqrt{2}, \frac{14}{3} \sqrt{5} \right) \) on the hyperbola, is equal to
- JEE Main - 2024
- Coordinate Geometry
- Two wires A and B are made up of the same material and have the same mass. Wire A has radius \(2.0 \, \text{mm}\) and wire B has radius \(4.0 \, \text{mm}\). The resistance of wire B is \(2 \, \Omega\). The resistance of wire A is _____ \( \Omega \).
- JEE Main - 2024
- Resistance
- A convex lens of focal length 40 cm forms an image of an extended source of light on a photo-electric cell. A current \( I \) is produced. The lens is replaced by another convex lens having the same diameter but focal length 20 cm. The photoelectric current now is:
- JEE Main - 2024
- Dual nature of matter
- For a sparingly soluble salt \( \text{AB}_2 \), the equilibrium concentrations of \( \text{A}^{2+} \) ions and \( \text{B}^- \) ions are \( 1.2 \times 10^{-4} \, \text{M} \) and \( 0.24 \times 10^{-3} \, \text{M} \), respectively. The solubility product of \( \text{AB}_2 \) is:
- JEE Main - 2024
- Method of Preparation of Diazoniun Salts
View More Questions
Concepts Used:
Uncertainty in Measurement
- Atoms and molecules consist of very low mass. But they are present in huge numbers.
- Chemists have to deal with numbers as large as 602,200,000,000,000,000,000,000, which is the number of molecules of 2g of hydrogen.
- There are even other constants like the speed of light, charges on particles, Avogadro’s number and etc.
- To handle these large or small numbers, we use the following notation: m × 10n, which is, m times ten raised to the power of n. In this expression, n is an exponent having positive and negative values and m is that number that varies from 1.000… and 9.999…
- The scientific notation 573.672 can be written as 5.73672 × 102 and in the same way, 0.000089 can also be written as 8.9 × 10-5.
- All of these help us to attain easier handling, better precision, and accuracy while performing operations on numbers with high magnitudes.
Read More: Uncertainty in Measurement