A coil of inductance 1 H and resistance 100Ω is connected to a battery of 6 V . Determine approximately : (a) The time elapsed before the current acquires half of its steady-state value (b) The energy

Question

A coil of inductance 1 H and resistance 100Ω is connected to a battery of 6 V . Determine approximately : (a) The time elapsed before the current acquires half of its steady-state value (b) The energy stored in the magnetic field associated with the coil at an instant 15 ms after the circuit is switched on. (Given ln 2 = 0.693 , e 2 − 3 ​ = 0.25 )

TestHub · Accepted Answer

Given circuit is R − L growth circuit The current is the circuit is given by, i = R E ​ ( 1 − e − τ t ​ ) For current to be half of the peak value, i = 2 R E ​ = R E ​ ( 1 − e − τ t ​ ) Solving t = τ ln 2 t = R L ​ ln 2 = 100 1 ​ 0.693 = 0.00693 ≃ 7 ms At time t = 15 ms , i ( 15 ms ) = R E ​ ( 1 − e − 10 15 ​ ) ⇒ i = 100 6 ​ ( 1 − 4 1 ​ ) = 4 3 ​ × 100 6 ​ = 0.045 A ⇒ U = 2 1 ​ L i 2 by solving we get U = 1 mJ .

Physics - EMI/AC Question with Solution | TestHub

Options:

Doubts & Discussion