Question

In terms Of line-to-line capacitance, the line-to-neutral capacitance of a single-phase transmission line is

(a) Same

(b) Twice

(c) One-half

Short answer

The correct option is (b): Twice

Step-by-step solution

Determine the expression for the line-to-line voltage.

The expression for single phase two wire line-to-line voltage is given by,

${\mathit{V}}_{\mathbf{x}\mathbf{y}}\mathbf{=}\frac{\mathbf{q}}{\mathbf{\pi }\mathbf{\epsilon }}\mathit{l}\mathit{n}\left(\frac{D}{\sqrt{r_x{r}_y}}\right)$

Here, q is the charge of the conductor, Dis the distance between the conductors, r_x and r_yare the radius of the conductors.

Determine the relationship between the line-to-line capacitance and line to neutral capacitance.

When the two-wire line is supplied by the grounded centre tap transformer, the voltage between the conductor and ground becomes the half.

$V_{xn}=\frac{V_{xy}}{2}$

The capacitance between the line to neutral is given by,

$C_n=\frac{q}{V_{xn}}$

Substitute $\frac{V_{xy}}{2}$ for V_xn into above equation.

$\begin{array}{rcl}{C}_n& =& \frac{q}{\frac{V_{xy}}{2}}\\ & =& 2\frac{q}{V_{xy}}\\ & =& 2C_{xy}\\ & & \end{array}$

Hence, the line to neutral capacitance is equal to the twice of the line-to-line capacitance.