An exchange uses a -40 V battery to drive subscriber lines. A resistance of 250 ohms is placed in series with the battery to protect it from short circuits. The subscribers are required to use a standard telephone set which offers a dc resistance of 50 ohms. The microphone requires 23mA for proper functioning given DC resistance of 133 ohms/km, find the farthest distance from the exchange at which the subscriber can be located.

Let R be the line loop resistance, by using the relation

I = V/R

The value of R can be determined as

23 x 10 = 40/ (250+50+R)

R = 1439

For 26 AWG wire R =133.89

Loop length= 1439/133.

Hence, the farthest distance at that the subscriber can be located is

10.74/2 = 5.37 km