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A battery is connected in series with a 0.34- resistor and an inductor, as shown

ID: 1440019 • Letter: A

Question

A battery is connected in series with a 0.34- resistor and an inductor, as shown in the figure below. The switch is closed at t = 0. The time constant of the circuit is 0.28 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

Resistance R = 0.34
The time constant of the circuit is = 0.28 s

The maximum current in the circuit is I = 8.2 A

(a) The emf of the battery E = IR

                                          = 2.788 V

(b) The inductance of the circuit L = R

                                                    = 95.2 x 10 - 3 H

                                                    = 95.2 mH

(c) The current in the circuit after one time constant has elapsed i = I [ 1- e -t / ]

Where t =

So, i = I [1-e -1]

        = 0.6321 I

        = 5.18 A

(d) The voltage across the resistor after one time constant V ' = i R

                                                                                              = 1.761 volt

The voltage across the inductor after one time constant has elapsed V " = E - V '

                                                                                                            = 1.0268 volt
resistor V

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