According to the formula R = ρ(L/A), where R is resistance, ρ is resistivity, L is length, and A is the cross-sectional area, resistance is directly proportional to length and inversely proportional to the cross-sectional area of the conductor.
14592
If the length of a copper wire is doubled while its cross-sectional area remains constant, how does its electrical resistance change?
The resistance (R) of a wire is directly proportional to its length (L) and inversely proportional to its cross-sectional area (A), given by R = ρ(L/A). If the length is doubled (2L) and the resistivity (ρ) and area (A) remain constant, the new resistance becomes R' = ρ(2L/A) = 2R. Therefore, the resistance doubles.
14593
What condition characterizes the formation of a short circuit in an electrical system?
A short circuit occurs when an electrical path with very low resistance is created between two points of different potential. This low resistance path allows an excessively high current to flow, which can lead to overheating or damage to the circuit components.
14594
Calculate the resistance of an electric bulb filament rated at 220 V and 100 W.
Using the power formula P = V^2 / R, we can rearrange to solve for resistance: R = V^2 / P. Substituting the given values: R = (220^2) / 100 = 48400 / 100 = 484 Ω. The closest provided option is 480 Ω, suggesting a rounding approximation in the source material.
14595
What is the standard SI unit for the electrical resistance of a conductor?
The SI unit for electrical resistance is the Ohm (Ω). While the question lists Ohm-metre, which is the unit for electrical resistivity, it is the closest option provided. Note: The standard unit for resistance is the Ohm, not the Ohm-metre.
14596
What is the typical electrical resistance of the human body under dry conditions?
The electrical resistance of the human body is highly variable and depends on factors such as skin moisture, contact area, and pressure. Under dry conditions, the outer layer of the skin (stratum corneum) provides significant resistance, often reaching up to 100,000 ohms. However, if the skin is wet or broken, this resistance drops dramatically, significantly increasing the risk of electric shock from low-voltage sources.
14597
How is Ohm's law mathematically expressed in a linear conductor?
Ohm's law states that the current flowing through a conductor between two points is directly proportional to the voltage across the two points. The constant of proportionality is the resistance (R). Thus, the relationship is defined by the equation V = IR, where V represents voltage, I represents current, and R represents resistance.
14598
What phenomenon occurs when a circuit is completed with an extremely low resistance path, allowing excessive current to flow?
A short circuit occurs when an electrical current follows a path of very low resistance, often due to a fault or accidental connection. According to Ohm's Law (I=V/R), as resistance approaches zero, the current increases dramatically, which can lead to overheating, damage to components, or fire hazards.
14599
An electric heater draws 4A of current at a potential difference of 60V. If the potential difference is increased to 165V, what will be the new current, assuming constant resistance?
First, calculate resistance: R = V/I = 60V / 4A = 15 ohms. Using this resistance for the new voltage: I = V_new / R = 165V / 15 ohms = 11A. The current increases proportionally with the voltage increase.
14600
If a shunt resistance of 12Ω reduces a galvanometer's deflection from 50 divisions to 25 divisions, what is the resistance of the galvanometer?
When a shunt resistance S is connected in parallel with a galvanometer of resistance G, the current divides. If the deflection is halved, the current through the galvanometer is halved, meaning the shunt resistance must be equal to the galvanometer resistance (G = S). Since S = 12Ω, G must also be 12Ω.
