Physics

An ammeter connected in an AC circuit measures the RMS (Root Mean Square) value of the current because RMS value represents the effective current that produces the same heating effect as a DC current of the same value.

The radius r of the circular path of a charged particle moving perpendicular to a uniform magnetic field is given by r = mv/(qB). This shows that r is directly proportional to the mass m, and inversely proportional to the charge q and magnetic field B. Therefore, the radius increases with increasing mass.

If A = B, then their dot products with their unit vectors should be equal, but A.B = A^ B^ is not a valid equality since A^ and B^ are unit vectors and the dot product of A and B is not equal to the product of their unit vectors. The other options correctly state properties that hold when A = B.

When an electron moves perpendicular to a uniform magnetic field, the magnetic force acts as a centripetal force, causing the electron to move in a circular path in the plane perpendicular to the field.

Electromechanical instruments are devices that combine electrical and mechanical components to measure or indicate electrical quantities. A galvanometer is an electromechanical instrument that measures small electric currents by deflecting a pointer. Voltmeters and ammeters are also electromechanical instruments, often using galvanometer mechanisms with additional components to measure voltage and current respectively. However, an AC transformer and a DC generator are electrical machines used to convert electrical energy or generate electricity, not instruments used for measurement. Therefore, the correct answer is D, as it is not an electromechanical instrument in the context of measurement devices.

The magnitude of vector A = 2i - 2j + k is calculated as √(2² + (-2)² + 1²) = √(4 + 4 + 1) = √9 = 3. The unit vector in the direction of A is the vector divided by its magnitude, which is (2i - 2j + k)/3. Therefore, the correct option is C.

In a parallel circuit, all components share the same two nodes, so the potential difference (voltage) across each component is the same regardless of their individual impedances. Therefore, the voltage across the inductor and capacitor connected in parallel is the same as the applied sinusoidal voltage.

When a charged particle enters a uniform magnetic field with a velocity component both perpendicular and parallel to the field, it undergoes circular motion perpendicular to the field and uniform motion parallel to the field, resulting in a helical (spiral) trajectory.

Two parallel wires carrying currents in opposite directions produce magnetic fields that cause the wires to repel each other due to the Lorentz force between the currents.

The magnetic force on a current-carrying wire is given by F = BIL sinθ. Here, θ = 90°, so sinθ = 1. Rearranging, I = F / (B * L) = 5 N / (0.5 T * 0.1 m) = 100 A.