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resistance of telephone line

A circuit consists of a 48 volt battery at a telephone company central office which is connected to a twisted pair telephone line. At the other end of the line is a telephone handset with a resistance of 1000 ohms. The twisted pair has a loop resistance of 100 ohms per kilometer. (Loop resistance is the combined resistance of the go and return wires.) Calculate the current in the circuit when:
a. The line is 10 km in length.
b. The line is 20 km in length
c. The minimum current required in the telephone circuit to ensure that the central office line relay closes when the subscriber's handset if off hook is 20 mA. What is the maximum length of the telephone line to meet this requirement?

Solution Preview

The ohm's law is: I = V/R

The circuit can be simplified as shown in the attached file.
The battery voltage V = 48 V
Let d be the length of the twisted telephone line. Its resistance is 100d ohms.
The total resistance of the ...

Solution Summary

It shows how to calculate the resistance of the telephone line and in turn finds the current in the circuit.