battery is connected in series with a 0.31- resistor and an inductor, as shown i

Question

battery is connected in series with a 0.31- resistor and an inductor, as shown in the figure below. The switch is closed at t = 0. The time constant of the circuit is 0.10 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. (Round your answer to four decimal places.) 
 A 

(d) Find the voltage across the resistor after one time constant has elapsed. (Round your answer to four decimal places.) 
 V 

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

Explanation / Answer

(a)
The maximum voltage over a long time period (> 10 * ) is
V = 8.2 A * 0.31 ohms = 2.542 Volts

(b) = 0.14 s = L / R = L / 0.32 ohms ;
L = 0.10 s * 0.31 ohms = 31.0E-3 Henrys = 31.0 milliHenrys

(c) V ( = 1) = (V * e^-(R/L * t)) / R = ( 2.542 * e^-1) / R = 0.2542 V / 0.31 = 0.82 Amps

(d) V = I * R = 0.82 Amps * 0.31 ohms = 0.2542 V

(e) V = VR + VL; 2.542 Volts =0.2542 V + VL ; VL = 2.2878 Volts

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