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..1 T-Mobile Wi-Fi ? 9:50 PM 76% GOAL Calculate a time constant and relate it to current in an RL circuit. PROBLEM A 12.6-V battery is in a circuit with a 30.0-mH inductor and a 0.150-? resistor. The switch is closed at t = 0. (a) Find the time constant of the circuit. (b) Find the current after one time constant has elapsed. (c) Find the voltage drops across the resistor when t 0 and t one time constant. (d) Whats the rate of change of the current after one time constant? STRATEGY Part (a) requires only substitution into the definition of time constant. With this value and Ohms law, the current after one time constant can be found, and multiplying this current by the resistance yields the voltage drop across the resistor after one time constant. With the voltage drop and Kirchhoffs loop law, the voltage across the inductor can be found. This value can be substituted into the proper equation to obtain the rate of change of the current. (A) Whats the time constant of the circuit? Subibitute the restance R into the equation, finding 15 200 (B) Find the current after one time constant has elapsed. use Ohms lawo ?-0.1900 . 84,0 A ome censtane, t the cument (0.632-(63284.0A) 53.1A (C) Find the voltage drops across the resistance when t-0 and t one time constant. nnaly the n the crout is using Chms law time constant (D) Whats the rate of change of the current after one time Using korchhos voltage nule, calculate the vetage drop across the inducto at for Allst and substnute 150 A/s
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