Consider a protected bus that terminates four lines, as shown in Figure 10.51. Assume that the linear couplers have the standard \(X_{m}=5 \mathrm{~m} \Omega\) and a three-phase fault externally located on line 3 causes the fault currents shown in Figure 10.51. Note that the infeed current on line 3 to the fault is \(-j 10 \mathrm{kA}\).

(a) Determine \(\mathrm{V}_{0}\).

(b) Let the fault be moved to an internal location on the protected bus between lines 3 and 4 . Find \(\mathrm{V}_{0}\) and discuss what happens.

(c) By moving the external fault from line 3 to a corresponding point on (i) line 2 and (ii) line 4, determine \(\mathrm{V}_{0}\) in each case.

-j16 KA 1 2 -j7 kA 4 Protected bus 3 4 -j36 kA -j13 KA X -j10 KA 10 V = ? +6 VR