A battery with voltage \(V\) sends a current \(I\) through a resistor \(R\). If \(V\) is quadrupled, \(I\) (A) stays the same. (B) quadruples. (C) halves. (D) doubles. (E) goes down by a factor of four.

Electric current is the flow of electric charge through a conductive material, typically measured in amperes (A). It's comparable to the flow of water through a pipe, with the charge being analogous to water molecules. An electric current is produced by a difference in electric potential or voltage across a conductor.

In simple terms, when we talk about electric current in a circuit, we are referring to the movement of electrons from one point to another due to the influence of an electric field, usually provided by a power source like a battery. A higher current implies a larger number of electrons are moving through the circuit.

It's important to understand that current is dependent on other factors, including voltage and resistance within the circuit. Ohm's law, which underpins the problem in question, is a fundamental rule that describes the relationship between these three aspects.

Electrical resistance is a material's opposition to the flow of electric current. This is similar to the friction that occurs when water flows through a pipe; it's a force that impedes the flow. In electrical terms, resistance is measured in ohms (\( \Omega \)) and varies based on a material's properties—such as its composition, temperature, and geometric dimensions.

A fundamental property of conductors (materials that allow current to flow easily) is that they have low resistance, while insulators (materials that block current flow) have high resistance. The value of resistance in a circuit determines how much current will flow for a given voltage. This relationship is precisely defined by Ohm's Law, which calculates current as a ratio of voltage to resistance.

The voltage-current relationship is a key component of Ohm’s Law, which states that the current (\( I \)) flowing through a conductor between two points is directly proportional to the voltage (\( V \)) across the two points and inversely proportional to the resistance (\( R \)). Expressed mathematically, it's \( I = \frac{V}{R} \). When voltage increases, current also increases, provided the resistance remains constant.

The exercise provided illustrates this principle perfectly. By quadrupling the voltage (\( V \)) while keeping the resistance (\( R \)) the same, the current (\( I \)) is also quadrupled. This concept is paramount in understanding how electrical devices operate and how to manipulate circuits to achieve desired currents and voltages.

It’s also worth noting that any changes to resistance in a circuit would likewise affect the current, but in this problem, as the resistance remains constant, the focus is solely on the impact of the change in voltage.