Electrical Engineering (EE) Exam > Electrical Engineering (EE) Questions > If the transmission line is lossless, then it...
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If the transmission line is lossless, then its characteristic will be _________
- a)√(L/C)
- b)√LC
- c)√(L+C)
- d)√(C/L)
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
If the transmission line is lossless, then its characteristic will be ...
The characteristic impedance for the lossless lines is given by √(L/C) because the resistance is zero.
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If the transmission line is lossless, then its characteristic will be ...
Understanding Characteristic Impedance
In transmission lines, the characteristic impedance (Z0) plays a vital role in determining how signals propagate along the line. For a lossless transmission line, it is defined as:
Formula for Characteristic Impedance
- The characteristic impedance (Z0) of a lossless transmission line is given by the formula:
- Z0 = √(L/C)
Where:
- L = Inductance per unit length (H/m)
- C = Capacitance per unit length (F/m)
Why Lossless Matters
- A lossless transmission line implies that there are no resistive losses (R = 0) and no dielectric losses (G = 0).
- This condition ensures that the energy is conserved and that the impedance remains purely reactive.
Analysis of Options
- Option A: √(L/C) - This is correct as it directly represents the characteristic impedance of a lossless transmission line.
- Option B: √(LC) - This does not represent characteristic impedance and is incorrect.
- Option C: √(L+C) - This is also incorrect as it does not relate to the properties of transmission lines.
- Option D: √(C/L) - This is not a standard representation of characteristic impedance and is incorrect.
Conclusion
In summary, the characteristic impedance of a lossless transmission line is determined by the square root of the inductance per unit length divided by the capacitance per unit length, confirming that option A (√(L/C)) is the correct answer. Understanding this concept is crucial for efficient signal transmission in electrical engineering applications.
In transmission lines, the characteristic impedance (Z0) plays a vital role in determining how signals propagate along the line. For a lossless transmission line, it is defined as:
Formula for Characteristic Impedance
- The characteristic impedance (Z0) of a lossless transmission line is given by the formula:
- Z0 = √(L/C)
Where:
- L = Inductance per unit length (H/m)
- C = Capacitance per unit length (F/m)
Why Lossless Matters
- A lossless transmission line implies that there are no resistive losses (R = 0) and no dielectric losses (G = 0).
- This condition ensures that the energy is conserved and that the impedance remains purely reactive.
Analysis of Options
- Option A: √(L/C) - This is correct as it directly represents the characteristic impedance of a lossless transmission line.
- Option B: √(LC) - This does not represent characteristic impedance and is incorrect.
- Option C: √(L+C) - This is also incorrect as it does not relate to the properties of transmission lines.
- Option D: √(C/L) - This is not a standard representation of characteristic impedance and is incorrect.
Conclusion
In summary, the characteristic impedance of a lossless transmission line is determined by the square root of the inductance per unit length divided by the capacitance per unit length, confirming that option A (√(L/C)) is the correct answer. Understanding this concept is crucial for efficient signal transmission in electrical engineering applications.
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