Physics – 4.5.6 The transformer | e-Consult

The equation P = I²R shows that power loss is directly proportional to the square of the current (I²). Voltage (V) and current are related by Ohm's Law: V = IR. Therefore, I = V/R. Substituting this into the power equation gives P = (V/R)²R = V²/R.

Since the resistance (R) of the cable is assumed to be constant, the power loss (P) is directly proportional to the square of the voltage (V²). This means that if the voltage is increased, the power loss will increase by a factor of the square of the voltage increase. However, if the voltage is *greater*, and the resistance is constant, the current will also be greater (due to Ohm's Law, V = IR). The key point is that the power loss is proportional to the *square* of the current. Therefore, if the voltage is increased, the current will increase, but the power loss will increase at a slower rate (proportional to the square of the current). In essence, a higher voltage allows for a higher current to be delivered with the same resistance, but the power loss is not as dramatically affected as it would be with a lower voltage and corresponding lower current. The increased voltage allows for more efficient transmission of power over a given distance, minimizing the relative impact of the resistance.