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An LR circuit has L = 1.0 H and R = 20 Ω. It is connected across an emf of 2.0 V at t = 0. Find di/dt at (a) t = 100 ms, )b) t = 200 ms and (c) t = 1.0 s.

An LR circuit has L = 1.0 H and R = 20 Ω. It is connected across an emf of 2.0 V at t = 0. Find di/dt at (a) t = 100 ms, )b) t = 200 ms and (c) t = 1.0 s.

Grade:upto college level

1 Answers

Aditi Chauhan
askIITians Faculty 396 Points
6 years ago
Sol. L = 1.0 H, R = 20 Ω , emf = 2.0 V Τ = L/R = 1/20 = 0.05 i base 0 = e/R = 2/20 = 0.1 A i = i base 0 (1 – e^-t ) = i base 0 – i base 0 e^-t ⇒ di/dt = di base 0/dt (i base 0 x – 1/τ x e^-t/τ) = i base 0 / τ e^-t/τ So, a) t = 100 ms ⇒ di/dt = 0.1/0.05 x e^-0.1/0.05 = 0.27 A (b) t = 200 ms ⇒ di/dt = 0.1/0.05 x e^-0.2/0.05 = 0.0366 A (c) t = 11 s ⇒ di/dt = 0.1/0.05 x e^-1/0.05 = 4x 10^-9 A

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