When a shunt resistor is connected in parallel with a galvanometer, the current divides between them. If the deflection is halved, it means the current through the galvanometer is equal to the current through the shunt. According to the parallel circuit rule, if the currents are equal, the resistances must be equal. Therefore, the galvanometer resistance equals the shunt resistance of 12Ω.

According to the formula R = ρ(L/A), resistance is inversely proportional to the cross-sectional area (A) of the wire, not directly proportional. A larger cross-sectional area provides more space for charge carriers to move, thereby reducing the resistance of the conductor.

The electrical resistivity of copper at approximately 20 degrees Celsius is widely accepted to be 1.69 × 10^-8 Ohm-meters. Resistivity is a measure of how strongly a material opposes the flow of electric current. This value confirms copper's status as an excellent conductor used extensively in electrical wiring.

The resistance of a conductor is influenced by several factors: the material's resistivity (nature), its geometric dimensions (length and cross-sectional area), and its physical state, including temperature and phase. All these parameters collectively determine the ease with which charge carriers can move through the material, thereby defining its total electrical resistance.

A rheostat is a variable resistor used to control the current in an electrical circuit. By adjusting the position of a sliding contact, the length of the resistive element in the circuit is changed, thereby varying the total resistance. According to Ohm's Law (I = V/R), increasing the resistance decreases the current, and decreasing the resistance increases the current.

A rheostat is a variable resistor used to control the flow of electric current by manually changing the resistance in a circuit. By adjusting the position of the sliding contact, the resistance can be varied, which in turn regulates the current or voltage signal in the circuit, making it a common tool for signal adjustment.

The Ohm (symbol: Ω) is the SI derived unit of electrical resistance. It is named after the German physicist Georg Simon Ohm. Resistance is a measure of the opposition to current flow in an electrical circuit. According to Ohm's Law, resistance is defined as the ratio of the voltage applied across a conductor to the current flowing through it (R = V/I).

According to Ohm's Law, I = V / R. Given V = 12 V and R = 100,000 Ω, the current I = 12 / 100,000 = 0.00012 A. Expressed in scientific notation, this is 1.2 × 10^-4 Amperes.

In residential electrical circuits, appliances are connected in parallel to ensure that each device receives the same full line voltage (typically 120V or 230V). This configuration also allows each appliance to be operated independently; if one device is switched off or fails, the others remain functional, as the circuit provides multiple paths for the current to flow.

In a series circuit, the current is the same through all components. Power dissipated is given by P = I^2 * R. Since the 40W bulb has the highest resistance (R = V^2/P), it dissipates the most power when the current is constrained by the series arrangement, causing it to glow brighter than the bulbs with lower resistance.