A battery is connected in series with a 0.28-? resistor and an inductor, as show

Question

A battery is connected in series with a 0.28-? resistor and an inductor, as shown in the figure below. The switch is closed at t = 0. The time constant of the circuit is 0.24 s, and the maximum current in the circuit is 8.2 A.

a) What is emf of the battery in V?

b) what is 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

(a)
The maximum voltage over a long time period (> 10 * ?) is
V = 8.2 A * 0.28 ohms = 2.296 Volts

V= 2.296 Volts

(b) ? = 0.24 s = L / R = L / 0.28 ohms ;
L = 0.24 s * 0.28 ohms = 0.0672 Henrys = 67.2 milliHenrys

L=67.2 milliHenrys

(c) V (? = 1) = (V * e^-(R/L * t)) / R = (2.296 * e^-1) / R

= 0.82 Amps

(d) V = I * R = 0.82 Amps * 0.28 ohms = 0.2296 V

(e) V = VR + VL; 2.296 Volts = 0.2296 V+ VL ; VL = 2.064 Volts

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