Question

Consider a three-core, three-phase, 50 Hz, 11 kV cable whose conductors are denoted as R, Y and B in the given figure. The inter-phase capacitance (C1) between each pair of conductors is 0.2 $\mu$F and the capacitance (C2) between each line conductor and the sheath is 0.4 $\mu$F.

 

• A. 2.0A
• B. 2.4A
• C. 2.7A
• D. 3.5A

Hint:

In 3-core cables, equivalent capacitance is taken as \( C_{\text{eq}} = C_2 + 3C_1 \). Always convert line voltage to phase voltage.

Answer 1

The Correct Option is A

Step 1: Capacitance in a 3-core cable
In a 3-phase system, the total charging current per phase is given by: \[ I = \omega V C_{\text{eq}} \] where \( C_{\text{eq}} = 3C_1 + C_2 \), and \( V \) is the phase voltage.
Step 2: Calculate phase voltage
Given line voltage \( V_L = 11\,\text{kV} \), phase voltage is: \[ V = \frac{11000}{\sqrt{3}} = 6350.85\,\text{V} \] Step 3: Total capacitance per phase
\[ C_{\text{eq}} = C_2 + 3C_1 = 0.4 + 3 \times 0.2 = 1.0\,\mu\text{F} \] Step 4: Calculate charging current
\[ I = 2\pi \times 50 \times 6350.85 \times 1 \times 10^{-6} \approx 2.0\,\text{A} \]