Acircuit consists of a coil that has a self-inductance equal to 4.3 mh and an internal resistance equal to 16 ω, an ideal 9 v battery, and an open switch--all connected in series. at t = 0 the switch is closed. find the time when the rate at which energy is dissipated in the coil equals the rate at which magnetic energy is stored in the coil.

t = 186.2 μs

Explanation:

Current in LR series circuit

----(1)

steady current =  I_{s} = V/R

time constant = τ =

                                              = 0.268 ms

magnetic energy stored in coil =

rate at which magnetic energy stored in coil= ----(2)

rate at which power is dissipated in R:

                                       ---(3)

To find the time when the rate at which energy is dissipated in the coil equals the rate at which magnetic energy is stored in the coil equate (2) and (3)

[/tex]I=\frac{L}{R}\frac{dI}{dt}[/tex]----(4)

differentiating (1) w.r.to t

---(5)

substituting (5) in (4)

----(6)

equating (1) and (6)

L= 4.3 mH

R= 16 Ω

t = 186.2 μs

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