The figure shows the lagging load phasor representation of a transmission line, where, V_S, R, X_L,V_R and I represent the sending end voltage, line resistance, line inductance, receiving end voltage and line current, respectively. Identify the transmission line which most suited for it.

Types of Transmission Lines Based on Voltage

1.) Short transmission lines - In short transmission lines, the length is within 50km and the voltage is limited to less than 20 kV. In short transmission lines, the effect of line resistance and inductance is more predominant than capacitance. 

2.) Medium transmission lines - These lines have an overhead cable length of greater than 50km and less than 150km. The allowable voltage ranges from 20 to 100 kV. The analysis of medium transmission lines considers the three lumped line constants: resistance, inductance, and capacitance.

3.) Long transmission lines - Overhead transmission lines with lengths greater than 150km and voltages above 100kV form long transmission lines. Line constants are considered distributed elements in the analysis of long transmission lines. 

Explanation

From the phasor diagram:

\(V_S=V_R+I_RR+jI_RX_L\)

\(V_S=V_R+I_R(R+jX_L)\)

\(V_S=V_R+I_RZ\)

and \(I_S=I_R\)

\(\begin{bmatrix} V_S\\ I_S \end{bmatrix}=\begin{bmatrix} 1 & z\\ 0 & 1 \end{bmatrix} \begin{bmatrix} V_R\\ I_R \end{bmatrix}\)

This represents a short transmission line.

Among the given option, 10 KV is the correct voltage level for a short transmission line.