Final answer:
The power dissipated in a transmission cable is inversely proportional to the square of the voltage, as a higher voltage allows for a smaller current, thereby reducing power loss due to Joule heating in the wire's resistance.
Step-by-step explanation:
The power dissipated in a transmission cable carrying current I and voltage V is inversely proportional to the square of the voltage, represented as V². This relationship is derived from two key equations. First, the power dissipated in a resistor is given by P = I²R, where P is power, I is current, and R is resistance. Secondly, for power transmitted along the cable, Ptransmitted = Itransmitted Vtransmitted.
To reduce power losses, which are manifested as heat (Joule heating) in the wire due to its resistance (Rwire), we should strive to have a lower current. This is achieved by transmitting power at a higher voltage, which allows for a smaller current and thereby less power dissipation due to the formula Plost = Itransmitted² Rwire. Hence, to minimize power loss (Plost), a higher voltage should be used so that lower current is required, in accordance with the relationship where power loss is inversely proportional to the square of the voltage due to the relationship between current, resistance, and power dissipation.