3 17 2014 Master It Master It A 140 mH inductor and a 4 55 resistor are connected with a switch to a 6 00 V battery as shown in the figure below a After the switch is first thrown to a connecting the battery what time interval elapses before the current reaches 220 mA b What is the current in the inductor 10 0 s after the switch is closed c Now the switch is quickly thrown from a to b What time interval elapses before the current in the inductor falls to 160 mA Part 1 of 6 Conceptualize The resistor limits the amount of current in the circuit The inductor limits the rate of increase of current after the battery is connected and the rate of decrease after it is switched off Calculating the time constant L R and using the currents given for the situations in parts a and b we can estimate the time intervals for the current to increase to the given value with the battery connected and for the current to decrease to the given value after the battery is disconnected The 10 0 s time interval is long enough that we expect the current to have nearly attained its maximum value of V R Part 2 of 6 Categorize We will use the equations for the increasing current in an LR circuit when the voltage is applied and for the exponentially decaying current when the voltage is switched off Part 3 of 6 Analyze a The equation for increasing current in an LR circuit is given by I 1 e Rt L R Solving for t we obtain the following http www webassign net v4cgi questions tutorial popup tpl 1 3 3 17 2014 Master It t L R ln 1 IR 0 14 H ln 1 0 22 A 4 55 4 55 6 00 V 5 62 ms Part 4 of 6 b Now we will use the general equation for I and substitute t 10 0 s Calculating the exponent in the 1 e Rt L equation I we have R R t L 4 55 0 14 H 1 H s 10 s 325 Part 5 of 6 We substitute the given values and the dimensionless value calculated above to obtain 6 00 V 1 e I 4 55 1 32 A 1 325 1 32 A Part 6 of 6 c The equation for the decrease in current after the battery is disconnected from the circuit is given by the following I R e Rt L Solving for t and substituting the given values we have t L R ln IR 0 14 H 6 00 V ln 4 55 0 16 A 4 55 64 9 ms Finalize We calculated the time interval after the switch is thrown for the current to attain a fraction about one fifth http www webassign net v4cgi questions tutorial popup tpl 2 3 3 17 2014 Master It of its maximum value Then we used a much larger time interval after the battery is connected to show that the current has nearly attained its maximum value After the battery is disconnected we found the time for the current to decay to about one tenth of its maximum value We found the time for the current to decay to be about eleven times longer than the time for the current to increase to the larger value The current increases faster after the switch is thrown than it decreases after the battery is disconnected http www webassign net v4cgi questions tutorial popup tpl 3 3
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