Question

Ordinary household electric lines in North America usually operate at 120 V . Why is this a desirable voltage, rather than a value considerably larger or smaller? On the other hand, automobiles usually have 12 V electrical systems. Why is this a desirable voltage?

Short answer

The households have long wires so keep the power the voltage must be kept high.But in the car the wires are small so the resistance is small so there is no need for high voltage.

Step-by-step solution

Power consumption of the electric circuit

Power $\mathbf{\left(}\mathbf{P}\mathbf{\right)}$in an electric circuit is exactly equal to current $\mathbf{\left(}\mathbf{I}\mathbf{\right)}$multiplied by voltage $\left(V\right)$.

_{$$\begin{gathered} \mathrm{P}=\mathrm{VI} \\ =\frac{{\mathrm{V}}^2}{\mathrm{R}} \end{gathered}$$}

Compare power consumption in household and automobile

The equation of power consumption of an electric circuit is

_{$\mathrm{P}=\frac{{\mathrm{V}}^2}{\mathrm{R}}$}

Since the households have long wires so keep the power the voltage must be kept high.

But in the car the wires are small so the resistance is small so there is no need for high voltage.