A coil having resistance 15 Ω and inductance 10 H is connected across a 90 Volt dc supply. Determine the value of current after 2 sec…

Q: A coil having resistance 15 Ω and inductance 10 H is connected across a 90 Volt dc supply. Determine the value of current after 2 sec. What is the energy stored in the magnetic field at that instant.

Sol: Give that; R = 15 Ω, L = 10 H, E = 90 Volt

Peak value of current , $\large I_0 = \frac{E}{R} = \frac{90}{15}$

= 6 A

Also , $\large \tau = \frac{L}{R} = \frac{10}{15} $

= 0.67 sec

$\large I = I_0 (1-e^{\frac{-Rt}{L}})$

After 2 sec ,

$\large I = 6 (1-e^{\frac{-2}{0.67}})$

= 6 (1-0.05) = 5.7 A

Energy stored in a magnetic field is

$\large U = \frac{1}{2}L I^2 $

$\large U = \frac{1}{2}\times 10(5.7)^2 $

= 162.45 J