An ideal battery with potential difference \(\Delta V\) is connected to four identical resistors, each with resistance \(R\), and a switch \(S\), as shown in the circuit diagram. Resistor \(R_1\) is in series with the battery, followed by two parallel branches: Branch A containing resistor \(R_2\), and Branch B containing resistors \(R_3\) and \(R_4\) in series. Switch \(S\) is connected in parallel across resistor \(R_3\).

Initially, switch \(S\) is open. Switch \(S\) is then closed, short-circuiting resistor \(R_3\). What is the ratio \(\dfrac{P_{\text{after}}}{P_{\text{before}}}\) of the total electric power delivered by the battery after switch \(S\) is closed to the total power delivered before switch \(S\) is closed?