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If the length of the cable is doubled, its capacitance C will become
Doubled
Half
One-fourth
Remain Unchanged
Doubled
The capacitance of a transmission line cable is directly proportional to its length. If the length of the cable is doubled, the total capacitance also doubles because the surface area of the cylindrical conductors increases.
The capacitance of a transmission line cable is directly proportional to its length. If the length of the cable is doubled, the total capacitance also doubles because the surface area of the cylindrical conductors increases.
C=ln(rRтАЛ)2╧А╧╡0тАЛ╧╡rтАЛlтАЛ тАФ Capacitance of a cylindrical cable
CтИЭl тАФ Linear proportionality to length
The capacitance C of a cable of length l is defined by the geometry of the conductors. For a cable with radius r and sheath radius R, the capacitance is C=ln(R/r)2╧А╧╡0тАЛ╧╡rтАЛlтАЛ. Since CтИЭl, any change in the length l results in a linearly proportional change in the total capacitance C.
Capacitance is a shunt parameter in transmission lines.
The permittivity of the insulating medium affects the absolute value of capacitance.
Increasing cable length increases the charging current required by the line.
This phenomenon is significant in underground cables due to higher shunt capacitance compared to overhead lines.
Predictable scaling of line parameters.
Easily measurable using impedance bridges.
Increases Ferranti effect in long transmission lines.
Higher capacitance leads to increased reactive power demand.
Transmission line modeling.
Cable insulation testing.
Power system steady-state analysis.
Capacitance of a line is defined in Farads (F), and per-unit length is F/m.
Option B (Half) would be correct for inductive reactance if it were inversely proportional, but capacitance scales directly.
A is correct тАФ The capacitance of a cable is directly proportional to its length; hence, doubling the length doubles the total capacitance.
Always remember that in transmission lines, shunt capacitance increases with length, whereas series resistance and series inductance also increase linearly with length.