<Dl> <Dd> P R = V 2 × I = V R R + R C × V R + R C = R R + R C × V 2 R + R C = R R + R C P V (\ displaystyle P_ (R) = V_ (2) \ times I = V (\ frac (R) (R + R_ (C))) \ times (\ frac (V) (R + R_ (C))) = (\ frac (R) (R + R_ (C))) \ times (\ frac (V ^ (2)) (R + R_ (C))) = (\ frac (R) (R + R_ (C))) P_ (V)) </Dd> </Dl> <Dd> P R = V 2 × I = V R R + R C × V R + R C = R R + R C × V 2 R + R C = R R + R C P V (\ displaystyle P_ (R) = V_ (2) \ times I = V (\ frac (R) (R + R_ (C))) \ times (\ frac (V) (R + R_ (C))) = (\ frac (R) (R + R_ (C))) \ times (\ frac (V ^ (2)) (R + R_ (C))) = (\ frac (R) (R + R_ (C))) P_ (V)) </Dd> <P> Assume now that a transformer converts high - voltage, low - current electricity transported by the wires into low - voltage, high - current electricity for use at the consumption point . If we suppose it is an ideal transformer with a voltage ratio of a (\ displaystyle a) (i.e., the voltage is divided by a (\ displaystyle a) and the current is multiplied by a (\ displaystyle a) in the secondary branch, compared to the primary branch), then the circuit is again equivalent to a voltage divider, but the transformer - consumption branch has an apparent resistance of a 2 R (\ displaystyle a ^ (2) R). The useful power is then: </P> <Dl> <Dd> P R = V 2 × I 2 = V 2 a 2 R + R C = a 2 R a 2 R + R C P V (\ displaystyle P_ (R) = V_ (2) \ times I_ (2) = (\ frac (V ^ (2)) (a ^ (2) R + R_ (C))) = (\ frac (a ^ (2) R) (a ^ (2) R + R_ (C))) P_ (V)) </Dd> </Dl>

Difference between electrical transmission lines and electrical distribution lines