Consider two resistors placed in series, one after the other, in an electric circuit connected to a battery with voltage V. Show that the effective resistance of the pair is R₁+R₂ by using the fact that the current through both resistors is the same while voltages add. Now connect the resistors in parallel, so that the voltage across both resistors is V. Compute the total current and show that the effective resistance satisfies 1/R = 1/R₁ + 1/R₂.