For an L-R circuit, the time constant equals:

twice the ratio of the energy stored in the magnetic field to the rate of energy dissipation in the resistance
the ratio of the energy stored in the magnetic field to the rate of energy dissipation in the resistance
half the ratio of the energy stored in the magnetic field to the rate of energy dissipation in the resistance
the square of the ratio of the energy stored in the magnetic field to the rate of energy dissipation in the resistance

Correct answer: twice the ratio of the energy stored in the magnetic field to the rate of energy dissipation in the resistance

Solution

tau = L/R. Energy stored in inductor U = (1/2)L*I²; power dissipated P = I²*R. So U/P = (1/2 L I²)/(I² R) = L/(2R) = tau/2. Therefore tau = 2*(U/P), i.e. twice the ratio of stored magnetic energy to the rate of dissipation.

Related JEE Main Physics questions

A metallic ring is kept in a horizontal position, and a bar magnet is released so that it falls through the ring with its length aligned along the ring’s axis. The magnet’s acceleration while falling is
A coil has resistance 10 Ω, and the magnetic flux linked with it changes with time according to ϕ = 4t² + 2t + 1 (in weber). The current induced in the coil at t = 1 s is
Two coils are kept near one another. The mutual inductance of the coil pair depends on
A conducting rod of length ℓ is attached to a string of length 2ℓ and is rotated on a horizontal table about the fixed end of the string with angular speed ω. If a uniform magnetic field B acts vertically through the region, what is the induced emf between the two ends of the rod?
A pair of coils, each having N turns, has mutual inductance M henry. If the current in one coil changes from 1 ampere to zero in time t seconds, what is the induced emf per turn in the other coil, in volts?
A boat travels straight toward the east in a place where Earth’s magnetic field is horizontal, points due north, and has magnitude 5.0 × 10⁻⁵ N A⁻¹ m⁻¹. A 2 m long vertical antenna is mounted on the boat. If the boat’s speed is 1.50 m s⁻¹, what emf is induced across the antenna wire?

⚔️ Practice JEE Main Physics free + battle 1v1 →