Electromagnetism Units Dimensions Mock Tests

A series LCR circuit has L = 1 H, C = 1 microfarad, and R = 1 ohm. The quality factor Q at resonance and the angular bandwidth Delta omega at half-power points are respectively:

A metallic rod of length L rotates with angular speed ω about one end in a plane perpendicular to a uniform magnetic field B. The emf induced between the pivot and the free end is:

Two identical small beads each of mass m and charge q are threaded on a frictionless circular hoop of radius R lying in a horizontal plane. The beads are released from rest and perform small oscillations about their equilibrium position (diametrically opposite). The square of the angular frequency omega^2 of small oscillations is: (k = 1/(4pi epsilon_0))

The period of oscillation T of a simple pendulum is given by T = 2π√(L/g). If the length L is measured as (100.0 ± 0.1) cm and the time for 100 oscillations is (200.0 ± 0.2) s, the percentage error in g is:

The fine structure constant α is a dimensionless quantity constructed from the elementary charge e, Planck constant h, speed of light c, and vacuum permittivity ε₀. The correct expression for α is:

A capacitor of capacitance C initially charged to voltage V_0 is connected at t = 0 through a resistor R to an ideal battery of emf epsilon in series. Taking the current direction as flowing from the battery through the resistor toward the capacitor, the current I(t) at time t is:

An LC circuit has L = 0.5 H and C = 2 µF. The capacitor is initially charged to 10 V and then connected to the inductor. The time taken for the capacitor to discharge completely for the first time is:

A parallel plate capacitor has plate area A and separation d. A dielectric slab of dielectric constant K and thickness d/2 is inserted between the plates, touching one plate. The capacitance of the modified capacitor is: