Electric Circuits - Mission EC8 Detailed Help

A 12-V battery and a 12-ohm resistor are connected as shown in circuit X below. A 6-ohm resistor is added to the 12-ohm resistor to create circuit Y as shown. The voltage drop across the 12-ohm resistor in circuit Y is ____ that across the resistor in X.

Voltage Drops in Parallel Circuits:
Electric charge encounters an energy gain as it passes through the battery. This energy boost means that it has also encountered an increase in electric potential. The amount of electric potential difference between the two terminals of the battery is equal to the voltage rating on the battery. The gain in electric potential made in the battery is lost by the charge when making the loop around the external circuit. In a parallel circuit, a single charge will only pass through a single resistor during this loop. Thus, the voltage gained by the charge in the battery is equal to the voltage drop across the resistor. This is true regardless of which resistor the charge passes through. Thus, all resistors must have the same voltage drop. This principle is expressed by the following mathematical statement:
∆Vbattery= ∆V= ∆V= ∆V

where ∆V1∆V2 and ∆V3 represent the voltage drop across the individual resistors.

Each circuit is powered by a battery of the same voltage (12 V). So the voltage drop across the single resistor in circuit X is equal to the battery voltage - 12 Volts. And the voltage drop across an individual branch in a parallel circuit is the equal to the battery voltage - 12 volts. Thus, every resistor in circuit X and circuit Y encounters a 12-volt electric potential difference.