# Power and power loss during transmission of power

So let's say power to be delivered to homes is 80 kW($$P_3$$ = 80 kW) and the houses have to receive it at 220 V ($$V_3$$ = 220 V). The substation is a 4000 V to 220 V step-down transformer and $$R_2=15\ \Omega$$.

It says that the power loss is $$I^2R$$, and I understand that here it has to be $$I_2^2R_2$$. But I'm confused about P=IV and V=IR, why is $$I_2^2R_2$$ not equal to $$I_2V_2$$? Why is $$V_2$$ not equal to $$I_2R_2$$? Could someone please explain what's going on here?

(Here the power loss is 60 kW so the power plant has to supply 140 kW (60 kW + 80 kW).) why is $$I^2_2R^2$$ not equal to $$I_2V_2$$?
Let $$V_2$$ be the (AC) voltage across at the source (left) end of the transmission lines. $$I_2R_2$$ is the voltage drop from the source end to the load (right) end. That is, the load end of the transmission line has voltage $$V_2 - I_2R_2$$ across which is lower than the source end.
The product $$I_2V_2$$ is the AC power (assuming unity power factor) delivered to the transmission lines. The product $$I_2(V_2 - I_2R_2)$$ is the power delivered to the step-down transformer which is lower than that delivered to the transmission lines. Thus, the power lost to heating the transmission lines is $$I^2_2R_2$$
• I have updated the image according to your suggestion. Is it true that now $V_a-V_b=I_2R_2$? Is $V_2=V_a$?