A battery is connected in series with a 0.27-? resistor and an inductor, as show

Question

A battery is connected in series with a 0.27-? resistor and an inductor, as shown in the figure below. The switch is closed at t = 0. The time constant of the circuit is 0.22 s, and the maximum current in the circuit is 8.2 A.

(a) Find the emf of the battery.
=________ V

(b) Find the inductance of the circuit.
=_________ mH

(c) Find the current in the circuit after one time constant has elapsed.
=__________ A

(d) Find the voltage across the resistor after one time constant has elapsed.
=________ V

(e) Find the voltage across the inductor after one time constant has elapsed.
=__________ V

Explanation / Answer

Hi, my friend a) Emf = V = Imax * R = 8.2 * 0.272 = 2.214 V b) since Time constant T = L/R therefore L = t * R = 0.22 sec * 0.27 = 59.4 mH c) After one time constant current rises to its 63% therefore after 1T ; I = 63% of Imax = 5.1824 d) after 1 time constant voltage drop across resistor is : V.D = 5.1824A * 0.27 = 1.399 V e) Since V= L* di/dt therefore voltage across inductor after 1 time constant is 0 Approx PLEASE RATE

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