Decay Of Current In An Lr Circuit

When an LR circuit is short-circuited, the inductor sustains the current, which decays exponentially as (I = I_0 e^{-t/\tau}), where the time constant (\tau = L/R) sets the pace of decay. The current falls to (1/e \approx 37%) of its initial value precisely when the elapsed time equals one time constant. Computing (\tau = L/R = 2/4 = 0.5) s, so the current reaches about 37 percent after 0.5 s. The option 2 s mistakenly uses the inductance value alone as the time constant. The option 8 s multiplies L by R instead of dividing. The option 0.25 s inverts the ratio to (R/L). This is the NCERT exponential-decay description of inductive transients, mirroring how charge decays on a discharging capacitor through an (RC) time constant. The decay law itself follows from solving (L,dI/dt + RI = 0), whose solution is a falling exponential with rate set by (R/L); during this decay the energy once stored in the magnetic field is gradually dissipated as heat in the resistance. A plausibility check confirms the units H/(\Omega) reduce to seconds, and a larger inductance or a smaller resistance would prolong the decay, consistent with the inductor's tendency to oppose any change in current; after roughly five time constants the current is essentially zero.