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For distilled water μ = μo , ε = 81εo and σ = 2 x 10-3 S/m, the ratio of conduction current density to displacement current density at 1 GHz is
- a)1.11 x 10-5
- b)4.44 x 10-4
- c)2.68 x 10-6
- d)1.68 x 10-7
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
For distilled waterμ =μo,ε = 81εoandσ = 2 x 1...
Given Parameters:
- Conductivity of distilled water, σ = 2 x 10^-3 S/m
- Permittivity of distilled water, ε = 81 ε0 (where ε0 is the vacuum permittivity)
To calculate the ratio of conduction current density to displacement current density at 1 GHz.
Formula:
The conduction current density, Jc can be calculated using Ohm's law as:
Jc = σE
where E is the electric field strength.
The displacement current density, Jd can be calculated using the Maxwell's equation as:
Jd = ε(dE/dt)
where dE/dt is the time derivative of electric field strength.
The ratio of conduction current density to displacement current density can be calculated as:
Jc/Jd = σ/(εω)
where ω is the angular frequency and is given as 2πf, where f is the frequency in Hz.
Calculation:
Given, ε = 81 ε0 and σ = 2 x 10^-3 S/m
At 1 GHz, ω = 2πf = 2π x 10^9 rad/s
Substituting the given values in the formula, we get:
Jc/Jd = σ/(εω) = 2 x 10^-3/(81 ε0 x 2π x 10^9) = 4.44 x 10^-4
Therefore, the ratio of conduction current density to displacement current density at 1 GHz is 4.44 x 10^-4, which is option B.
- Conductivity of distilled water, σ = 2 x 10^-3 S/m
- Permittivity of distilled water, ε = 81 ε0 (where ε0 is the vacuum permittivity)
To calculate the ratio of conduction current density to displacement current density at 1 GHz.
Formula:
The conduction current density, Jc can be calculated using Ohm's law as:
Jc = σE
where E is the electric field strength.
The displacement current density, Jd can be calculated using the Maxwell's equation as:
Jd = ε(dE/dt)
where dE/dt is the time derivative of electric field strength.
The ratio of conduction current density to displacement current density can be calculated as:
Jc/Jd = σ/(εω)
where ω is the angular frequency and is given as 2πf, where f is the frequency in Hz.
Calculation:
Given, ε = 81 ε0 and σ = 2 x 10^-3 S/m
At 1 GHz, ω = 2πf = 2π x 10^9 rad/s
Substituting the given values in the formula, we get:
Jc/Jd = σ/(εω) = 2 x 10^-3/(81 ε0 x 2π x 10^9) = 4.44 x 10^-4
Therefore, the ratio of conduction current density to displacement current density at 1 GHz is 4.44 x 10^-4, which is option B.
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For distilled waterμ =μo,ε = 81εoandσ = 2 x 10-3S/m, the ratio of conduction current density to displacement current density at 1 GHz isa)1.11 x 10-5b)4.44 x 10-4c)2.68 x 10-6d)1.68 x 10-7Correct answer is option 'B'. Can you explain this answer?
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For distilled waterμ =μo,ε = 81εoandσ = 2 x 10-3S/m, the ratio of conduction current density to displacement current density at 1 GHz isa)1.11 x 10-5b)4.44 x 10-4c)2.68 x 10-6d)1.68 x 10-7Correct answer is option 'B'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about For distilled waterμ =μo,ε = 81εoandσ = 2 x 10-3S/m, the ratio of conduction current density to displacement current density at 1 GHz isa)1.11 x 10-5b)4.44 x 10-4c)2.68 x 10-6d)1.68 x 10-7Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For distilled waterμ =μo,ε = 81εoandσ = 2 x 10-3S/m, the ratio of conduction current density to displacement current density at 1 GHz isa)1.11 x 10-5b)4.44 x 10-4c)2.68 x 10-6d)1.68 x 10-7Correct answer is option 'B'. Can you explain this answer?.
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