GATE Exam > GATE Questions > A uniform silver wire has a resistivity of 1....
Start Learning for Free
A uniform silver wire has a resistivity of 1.54 x 10-8 Clm at room temperature and there are 5.8 x 1028 conduction electrons per m3. If an electric field of 1 volt cm is applied along the wire, the relaxation time of electron will be
- a)3.97x10-14 s
- b)3.97x10-15 s
- c)3.97x10-13 s
- d)3.97x10-16 s
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
A uniform silver wire has a resistivity of 1.54 x 10-8Clm at room temp...
Mobility, 
Relaxation time τ is given by
Relaxation time τ is given by
Most Upvoted Answer
A uniform silver wire has a resistivity of 1.54 x 10-8Clm at room temp...
Given data:
- Resistivity of silver wire = 1.54 x 10^-8 Ωm
- Number of conduction electrons per m^3 = 5.8 x 10^28 electrons/m^3
- Electric field applied = 1 V/cm
To find: Relaxation time of electron
Formula used:
- Resistivity (ρ) = (m/ne^2)τ
where m = mass of electron, n = number of electrons per unit volume, e = charge of electron, and τ = relaxation time
- Electric current density (J) = nev
where J = current density, n = number of electrons per unit volume, e = charge of electron, and v = drift velocity
- Drift velocity (v) = (eEτ)/m
where E = electric field strength
Calculation:
- Mass of electron (m) = 9.1 x 10^-31 kg
- Charge of electron (e) = 1.6 x 10^-19 C
- Electric field strength (E) = 1 V/cm = 100 V/m
- Number of electrons per unit volume (n) = 5.8 x 10^28 electrons/m^3
- Electric current density (J) = nev = ne(eEτ)/m
- Resistivity (ρ) = (m/ne^2)τ
=> τ = (m/ne^2)ρ
=> τ = (9.1 x 10^-31)/(5.8 x 10^28 x (1.6 x 10^-19)^2 x 1.54 x 10^-8)
=> τ = 3.97 x 10^-14 s
Therefore, the relaxation time of electron is 3.97 x 10^-14 s (Option A).
- Resistivity of silver wire = 1.54 x 10^-8 Ωm
- Number of conduction electrons per m^3 = 5.8 x 10^28 electrons/m^3
- Electric field applied = 1 V/cm
To find: Relaxation time of electron
Formula used:
- Resistivity (ρ) = (m/ne^2)τ
where m = mass of electron, n = number of electrons per unit volume, e = charge of electron, and τ = relaxation time
- Electric current density (J) = nev
where J = current density, n = number of electrons per unit volume, e = charge of electron, and v = drift velocity
- Drift velocity (v) = (eEτ)/m
where E = electric field strength
Calculation:
- Mass of electron (m) = 9.1 x 10^-31 kg
- Charge of electron (e) = 1.6 x 10^-19 C
- Electric field strength (E) = 1 V/cm = 100 V/m
- Number of electrons per unit volume (n) = 5.8 x 10^28 electrons/m^3
- Electric current density (J) = nev = ne(eEτ)/m
- Resistivity (ρ) = (m/ne^2)τ
=> τ = (m/ne^2)ρ
=> τ = (9.1 x 10^-31)/(5.8 x 10^28 x (1.6 x 10^-19)^2 x 1.54 x 10^-8)
=> τ = 3.97 x 10^-14 s
Therefore, the relaxation time of electron is 3.97 x 10^-14 s (Option A).
|
Explore Courses for GATE exam
|
|
Similar GATE Doubts
A uniform silver wire has a resistivity of 1.54 x 10-8Clm at room temperature and there are 5.8 x 1028conduction electrons per m3. If an electric field of 1 volt cm is applied along the wire, the relaxation time of electron will bea)3.97x10-14sb)3.97x10-15sc)3.97x10-13sd)3.97x10-16sCorrect answer is option 'A'. Can you explain this answer?
Question Description
A uniform silver wire has a resistivity of 1.54 x 10-8Clm at room temperature and there are 5.8 x 1028conduction electrons per m3. If an electric field of 1 volt cm is applied along the wire, the relaxation time of electron will bea)3.97x10-14sb)3.97x10-15sc)3.97x10-13sd)3.97x10-16sCorrect answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A uniform silver wire has a resistivity of 1.54 x 10-8Clm at room temperature and there are 5.8 x 1028conduction electrons per m3. If an electric field of 1 volt cm is applied along the wire, the relaxation time of electron will bea)3.97x10-14sb)3.97x10-15sc)3.97x10-13sd)3.97x10-16sCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A uniform silver wire has a resistivity of 1.54 x 10-8Clm at room temperature and there are 5.8 x 1028conduction electrons per m3. If an electric field of 1 volt cm is applied along the wire, the relaxation time of electron will bea)3.97x10-14sb)3.97x10-15sc)3.97x10-13sd)3.97x10-16sCorrect answer is option 'A'. Can you explain this answer?.
A uniform silver wire has a resistivity of 1.54 x 10-8Clm at room temperature and there are 5.8 x 1028conduction electrons per m3. If an electric field of 1 volt cm is applied along the wire, the relaxation time of electron will bea)3.97x10-14sb)3.97x10-15sc)3.97x10-13sd)3.97x10-16sCorrect answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A uniform silver wire has a resistivity of 1.54 x 10-8Clm at room temperature and there are 5.8 x 1028conduction electrons per m3. If an electric field of 1 volt cm is applied along the wire, the relaxation time of electron will bea)3.97x10-14sb)3.97x10-15sc)3.97x10-13sd)3.97x10-16sCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A uniform silver wire has a resistivity of 1.54 x 10-8Clm at room temperature and there are 5.8 x 1028conduction electrons per m3. If an electric field of 1 volt cm is applied along the wire, the relaxation time of electron will bea)3.97x10-14sb)3.97x10-15sc)3.97x10-13sd)3.97x10-16sCorrect answer is option 'A'. Can you explain this answer?.
Solutions for A uniform silver wire has a resistivity of 1.54 x 10-8Clm at room temperature and there are 5.8 x 1028conduction electrons per m3. If an electric field of 1 volt cm is applied along the wire, the relaxation time of electron will bea)3.97x10-14sb)3.97x10-15sc)3.97x10-13sd)3.97x10-16sCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
Download more important topics, notes, lectures and mock test series for GATE Exam by signing up for free.
Here you can find the meaning of A uniform silver wire has a resistivity of 1.54 x 10-8Clm at room temperature and there are 5.8 x 1028conduction electrons per m3. If an electric field of 1 volt cm is applied along the wire, the relaxation time of electron will bea)3.97x10-14sb)3.97x10-15sc)3.97x10-13sd)3.97x10-16sCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A uniform silver wire has a resistivity of 1.54 x 10-8Clm at room temperature and there are 5.8 x 1028conduction electrons per m3. If an electric field of 1 volt cm is applied along the wire, the relaxation time of electron will bea)3.97x10-14sb)3.97x10-15sc)3.97x10-13sd)3.97x10-16sCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for A uniform silver wire has a resistivity of 1.54 x 10-8Clm at room temperature and there are 5.8 x 1028conduction electrons per m3. If an electric field of 1 volt cm is applied along the wire, the relaxation time of electron will bea)3.97x10-14sb)3.97x10-15sc)3.97x10-13sd)3.97x10-16sCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of A uniform silver wire has a resistivity of 1.54 x 10-8Clm at room temperature and there are 5.8 x 1028conduction electrons per m3. If an electric field of 1 volt cm is applied along the wire, the relaxation time of electron will bea)3.97x10-14sb)3.97x10-15sc)3.97x10-13sd)3.97x10-16sCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A uniform silver wire has a resistivity of 1.54 x 10-8Clm at room temperature and there are 5.8 x 1028conduction electrons per m3. If an electric field of 1 volt cm is applied along the wire, the relaxation time of electron will bea)3.97x10-14sb)3.97x10-15sc)3.97x10-13sd)3.97x10-16sCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice GATE tests.
|
|
Explore Courses for GATE exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup