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The surge impedance of a 50-mile-long underground cable is 50 ohms. It will be _________ for a length of 25 miles.
- a)95 ohm
- b)80 ohm
- c)50 ohm
- d)40 ohm
Correct answer is option 'C'. Can you explain this answer?
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The surge impedance of a 50-mile-long underground cable is 50 ohms. It...
Surge impedance:
The surge impedance or characteristic impedance of a long transmission line is given by,
Where,
Z is series impedance per unit length per phase
Y is shunt admittance per unit length per phase
In case of a lossless line (i.e. R = 0, G = 0), the surge impedance is given by
- Surge impedance does not depend upon the length of the transmission line.
- Surge impedance depends on the characteristics of the transmission line like diameter & spacing between the conductors.
- So that surge impedance of 50 miles and 25 miles long underground cable is 50 Ω.
Important Points
Surge impedance loading (SIL):
Surge impedance loading is defined as the power load in which the total reactive power of the lines becomes zero. The reactive power generated by the shunt capacitance is consumed by the series inductance of the line.
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The surge impedance of a 50-mile-long underground cable is 50 ohms. It...
Surge Impedance of a 50-mile-long underground cable
The surge impedance of a transmission line is a characteristic property that determines the behavior of electrical signals traveling through the line. It is defined as the ratio of the voltage to the current in a traveling wave on the line.
Given:
Length of the underground cable = 50 miles
Surge impedance of the cable = 50 ohms
Calculating the surge impedance:
The surge impedance of a transmission line is given by the formula:
Zs = sqrt(L/C)
Where,
Zs is the surge impedance
L is the inductance per unit length of the line
C is the capacitance per unit length of the line
To find the surge impedance, we need to calculate the inductance and capacitance per unit length of the cable.
Calculating inductance per unit length:
Inductance is determined by the geometrical and material properties of the cable. It can be calculated using the formula:
L = (μ0μr/2π) * ln(D/d)
Where,
L is the inductance per unit length
μ0 is the permeability of free space (4π × 10^-7 H/m)
μr is the relative permeability of the cable material
D is the outer diameter of the cable
d is the inner diameter of the cable
Calculating capacitance per unit length:
Capacitance is determined by the geometrical and material properties of the cable. It can be calculated using the formula:
C = (2πεr/ln(D/d)) * ε0
Where,
C is the capacitance per unit length
ε0 is the permittivity of free space (8.854 × 10^-12 F/m)
εr is the relative permittivity of the cable material
D is the outer diameter of the cable
d is the inner diameter of the cable
Calculating surge impedance:
Once we have calculated the inductance and capacitance per unit length, we can substitute these values into the surge impedance formula:
Zs = sqrt(L/C)
Calculating surge impedance for a length of 25 miles:
Since the surge impedance is a characteristic property of the cable, it remains the same regardless of the length of the cable. Therefore, the surge impedance for a length of 25 miles will also be 50 ohms.
Answer:
Therefore, the surge impedance for a length of 25 miles is 50 ohms. (Option C)
The surge impedance of a transmission line is a characteristic property that determines the behavior of electrical signals traveling through the line. It is defined as the ratio of the voltage to the current in a traveling wave on the line.
Given:
Length of the underground cable = 50 miles
Surge impedance of the cable = 50 ohms
Calculating the surge impedance:
The surge impedance of a transmission line is given by the formula:
Zs = sqrt(L/C)
Where,
Zs is the surge impedance
L is the inductance per unit length of the line
C is the capacitance per unit length of the line
To find the surge impedance, we need to calculate the inductance and capacitance per unit length of the cable.
Calculating inductance per unit length:
Inductance is determined by the geometrical and material properties of the cable. It can be calculated using the formula:
L = (μ0μr/2π) * ln(D/d)
Where,
L is the inductance per unit length
μ0 is the permeability of free space (4π × 10^-7 H/m)
μr is the relative permeability of the cable material
D is the outer diameter of the cable
d is the inner diameter of the cable
Calculating capacitance per unit length:
Capacitance is determined by the geometrical and material properties of the cable. It can be calculated using the formula:
C = (2πεr/ln(D/d)) * ε0
Where,
C is the capacitance per unit length
ε0 is the permittivity of free space (8.854 × 10^-12 F/m)
εr is the relative permittivity of the cable material
D is the outer diameter of the cable
d is the inner diameter of the cable
Calculating surge impedance:
Once we have calculated the inductance and capacitance per unit length, we can substitute these values into the surge impedance formula:
Zs = sqrt(L/C)
Calculating surge impedance for a length of 25 miles:
Since the surge impedance is a characteristic property of the cable, it remains the same regardless of the length of the cable. Therefore, the surge impedance for a length of 25 miles will also be 50 ohms.
Answer:
Therefore, the surge impedance for a length of 25 miles is 50 ohms. (Option C)
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The surge impedance of a 50-mile-long underground cable is 50 ohms. It will be _________ for a length of 25 miles.a)95 ohmb)80 ohmc)50 ohmd)40 ohmCorrect answer is option 'C'. Can you explain this answer?
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