An emf of 20 V is applied at time t = 0 to a circuit containing in series 10 m H inductor and 5Ω resistor. The ratio of the currents at time t = ∞ and at t = 40 s is close to: (Take e 2 = 7.389 )

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i = i 0 ​ ( 1 − e L / R − t ​ ) = 5 20 ​ ( 1 − e 0.01/5 − t ​ ) = 4 ( 1 − e − 500 t ) now at t = ∞ i ∞ ​ = 4 at t = 40 s i 40 ​ = 4 ( 1 − e − 500 × 40 ) = 4 ( 1 − ( e 2 ) 10000 1 ​ ) = 4 ( 1 − 7.2 9 10000 1 ​ ) i 40 ​ i ∞ ​ ​ ≈ 1 Slightly greater then one.

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