Power is transmitted at 80 kV between two stations. If the...

Power is transmitted at $80 \mathrm{kV}$ between two stations. If the voltage can be increased to $160 \mathrm{kV}$ without a change in cable size, how much additional power can be transmitted for the same current? What effect does the power increase have on the line heating loss?

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Key Concepts

Joule Heating Losses

Joule heating losses, calculated as I²R, represent the power lost as heat in the transmission line due to the resistance of the cable. When the current remains constant, these losses remain unchanged regardless of changes in voltage. Thus, increasing the voltage increases the transmitted power without affecting the magnitude of the heating losses, so long as the current and resistance of the cable remain the same.

Electrical Power Transmission

This concept involves transferring electrical energy over long distances using transmission lines. It includes factors such as voltage level, current, and resistance of the cables. High voltage transmission is often used to reduce losses due to the finite resistance of conductors, thereby allowing more power to be transmitted efficiently over long distances.

Voltage and Current Relationship

The fundamental relation P = V × I shows that power transmitted depends directly on both the voltage and the current. By increasing the voltage while maintaining the same current, the total transmitted power increases proportionally. This means that for a given current, higher voltage levels result in greater power transmission.

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