Question: The potential difference E (in V) between a telegraph line and earth is given by where A and B are constants, x is the distance

The potential difference E (in V) between a telegraph line and earth is given by

( * =) * VR E = A cosh x + Bsinh| x VR

where A and B are constants, x is the distance in km from the transmitting end, r is the resistance per km of the conductor and R is the insulation resistance per km. Find the values of A and B when the length of the line is 400 km, r = 8Ω, R = 3.2 × 10⁷ and the voltages at the transmitting and receiving ends are 250 and 200 V respectively.

( * =) * VR E = A cosh x + Bsinh| x VR

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