The resistance of a wire is given by R = ρL/A, where A = πr². If the radius r is doubled, the area A becomes 4 times larger. Since resistance is inversely proportional to the cross-sectional area, the new resistance becomes R/4. Thus, 9 Ω / 4 = 2.25 Ω.

Ohm's Law states that the current flowing through a conductor between two points is directly proportional to the voltage across the two points, provided the temperature and other physical conditions remain constant. This linear relationship is characteristic of ohmic conductors, such as metallic wires, whereas semiconductors and insulators exhibit non-linear current-voltage characteristics.

Resistance is inversely proportional to the cross-sectional area of a wire (R = ρL/A). Therefore, stating that resistance is directly proportional to the area is physically incorrect, making option C the false statement.

A voltmeter is an instrument used to measure the electric potential difference between two points in an electric circuit. It is connected in parallel with the component across which the voltage drop is being measured.

According to Ohm's Law, I = V / R. Given the voltage V = 12V and resistance R = 100,000Ω (10^5 Ω), the current I = 12 / 100,000 = 0.00012 Amperes. Expressed in scientific notation, this is 1.2 × 10^-4 Amperes. This calculation demonstrates the relationship between potential difference and resistance in determining the magnitude of current flow.

An ammeter is designed to measure the flow of electric charge. To ensure that the entire current of the circuit passes through the meter, it must be connected in series with the load. Because ammeters are designed to have very low internal resistance, placing them in series minimizes the impact on the circuit's total resistance, allowing for an accurate measurement of the current flowing through that branch.

Kirchhoff's Voltage Law (KVL) states that the sum of potential changes around a closed loop is zero. This is a direct consequence of the law of conservation of energy. Since electric potential is defined as potential energy per unit charge, a closed loop implies that a charge returning to its starting point must have the same potential energy, meaning no net energy is gained or lost.

In a parallel circuit, the voltage across each component is the same, but the total current supplied by the source is divided among the branches. According to Kirchhoff's Current Law, the sum of the currents entering a junction must equal the sum of the currents leaving it, meaning the total current is the sum of the individual branch currents.

Kirchhoff's second rule, also known as the voltage law, states that the algebraic sum of all potential differences (voltage drops across resistors and electromotive forces from batteries) around any closed loop in an electrical circuit must equal zero. This is a direct consequence of the conservation of energy within the circuit.

Kirchhoff's First Law, also known as the Current Law or Junction Rule, is based on the principle of conservation of charge. It asserts that at any node in an electrical circuit, the total algebraic sum of currents is zero, meaning charge cannot accumulate at the junction.