Electrical Power Systems

54 Electrical Power Systems
moving a unit charge of one coulomb from X 2 to X 1, through the electric field produced by the
charge on the conductor.
Therefore,
\ V 12 =
D2
z y
D2
z
D1
D1
V12 = E . dy =
HG
q
2p
Î
o
y dy
q D2
ln
2pÎ
D
Volts ...(3.2)
o
1
I
KJ
V 12 is the voltage at X 1 with respect to X 2. V 12 is positive, when q is positive and D 2 > D 1, i.e.,
X 1 is at higher potential than X 2. or alternating current, V 12 is a phasor voltage and q is a
phasor representation of a sinusoidal charge.
3.2 POTENTIAL DIERENCE IN AN ARRAY O SOLID
CYLINDRICAL CONDUCTORS
ig. 3.2: Array of N conductors.
Neglecting the distortion effect and assuming that the charge is uniformly distributed
around the conductor, with the following constraint.
q 1 + q 2 + ... + q N = 0...(3.3)
Now apply eqn. (3.2) to the multiconductor configuration shown in ig. 3.2. Assume conductor
m has a charge q m coulomb/m. The potential difference V Ki(q m) between conductors K and i due
to the charge q m alone is
V Ki (q m)=
qmDim ln Volt ...(3.4)
2p Î D
o
HG
Km
When K = m or i = m, D mm = r m. Using superposition, the potential difference between
conductors K and i due to the all charges is
I
KJ