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The value of constant A of transmission line
Increases with the increase in length of line
Decreases with the increase in length of line
Is independent of length of line
Is dependent on length of line
Increases with the increase in length of line
In a transmission line model, the ABCD parameters define the relationship between the sending-end and receiving-end voltage and current. The constant A is a complex quantity that characterizes the line's impedance and admittance, and its magnitude is a hyperbolic function of the line's length.
In a transmission line model, the ABCD parameters define the relationship between the sending-end and receiving-end voltage and current. The constant A is a complex quantity that characterizes the line's impedance and admittance, and its magnitude is a hyperbolic function of the line's length.
A=cosh(╬│l) тАФ Exact definition for a long transmission line
AтЙИ1+2ZYтАЛ тАФ Approximation for a medium transmission line
According to the transmission line equations for a long line, A=cosh(╬│l), where ╬│=zyтАЛ is the propagation constant and l is the length of the line. As the length l increases, the value of cosh(╬│l) increases. For short and medium lines, this can be approximated using series expansion, where terms involving l lead to an increase in the value of constant A.
A is a dimensionless complex constant representing the ratio of sending-end voltage to receiving-end voltage under open-circuit conditions.
For a lossless line, A becomes cos(╬▓l), where ╬▓ is the phase constant.
A is equal to D for a symmetrical transmission line.
As length increases, the line moves from short to medium to long, causing the magnitude of A to increase from unity.
Simplifies calculation of system stability
Provides a standardized way to characterize different voltage levels
Becomes complex to compute for very long lines without approximation
Dependency on frequency complicates constant A analysis
Power system load flow studies
Fault analysis in high voltage networks
For a short transmission line (l<80 km), A is approximately 1, making it virtually independent of length for very short lines, but generally it is dependent.
Option B is incorrect because the hyperbolic function growth dominates over any potential reduction factors in standard transmission models.
A is correct тАФ The constant A follows the hyperbolic relation A=cosh(╬│l), resulting in an increase in its value as the transmission line length increases.
Always remember that for any symmetrical network, A=D and ADтИТBC=1; these properties are frequently used in competitive exams to solve for unknowns in a two-port network.