\"font-family:\'trebuchet MS\', Arial;font-size:13px;\">A circuit is constructed

Question

"font-family:'trebuchet MS', Arial;font-size:13px;">A circuit is

constructed with four resistors, one inductor, one battery and a

switch as shown. The values for the resistors are:

R

"font-family:'trebuchet MS', Arial;">1

"font-family:'trebuchet MS', Arial;font-size:13px;"> =

R

"font-family:'trebuchet MS', Arial;">2

"font-family:'trebuchet MS', Arial;font-size:13px;"> = 59 ?,

R

"font-family:'trebuchet MS', Arial;">3

"font-family:'trebuchet MS', Arial;font-size:13px;"> = 88 ?

and R

"font-family:'trebuchet MS', Arial;">4

"font-family:'trebuchet MS', Arial;font-size:13px;"> = 113 ?.

The inductance is L = 462 mH and the battery voltage is V = 24

V.

"https://www.smartphysics.com/Content/Media/Images/EM/18/h18_RL_limits.png"

alt="h18_RL_limits" />

"margin-right:4px;margin-bottom:8px;margin-left:0px;padding:0px;border:0px;font-size:13px;vertical-align:baseline;float:left;font-family:'trebuchet MS', Arial;">

1)

The

switch has been open for a long time when at time t = 0, the switch

is closed. What is I

"font-family:'trebuchet MS', Arial;">1

"font-family:'trebuchet MS', Arial;font-size:13px;">(0), the

magnitude of the current through the resistor R

"font-family:'trebuchet MS', Arial;">1

"font-family:'trebuchet MS', Arial;font-size:13px;"> just

after the switch is closed?

"font-family:'trebuchet MS', Arial;font-size:13px;">2)

What

is I

"font-family:'trebuchet MS', Arial;">1

"font-family:'trebuchet MS', Arial;font-size:13px;">(?), the

magnitude of the current that flows through the resistor

R

"font-family:'trebuchet MS', Arial;">1

"font-family:'trebuchet MS', Arial;font-size:13px;"> a very

long time after the switch has been closed?

"margin-right:4px;margin-bottom:8px;margin-left:0px;padding:0px;border:0px;font-size:13px;vertical-align:baseline;float:left;font-family:'trebuchet MS', Arial;">

3)

"font-family:'trebuchet MS', Arial;font-size:13px;">What is

V

"font-family:'trebuchet MS', Arial;">L

"font-family:'trebuchet MS', Arial;font-size:13px;">(0), the

magnitude of the voltage across the inductor just after the switch

is closed?

"margin-right:4px;margin-bottom:8px;margin-left:0px;padding:0px;border:0px;font-size:13px;vertical-align:baseline;float:left;font-family:'trebuchet MS', Arial;">

4)

"font-family:'trebuchet MS', Arial;font-size:13px;">What is

I

"font-family:'trebuchet MS', Arial;">L

"font-family:'trebuchet MS', Arial;font-size:13px;">(?), the

magnitude of the current through the inductor after the switch has

been closed for a very long time?

"margin-right:4px;margin-bottom:8px;margin-left:0px;padding:0px;border:0px;font-size:13px;vertical-align:baseline;float:left;font-family:'trebuchet MS', Arial;">

5)

"font-family:'trebuchet MS', Arial;font-size:13px;">What is

I

"font-family:'trebuchet MS', Arial;">2

"font-family:'trebuchet MS', Arial;font-size:13px;">(0), the

magnitude of the current through the resistor R

"font-family:'trebuchet MS', Arial;">2

"font-family:'trebuchet MS', Arial;font-size:13px;"> just

after the switch is closed?

Explanation / Answer

TAKING R1=R2= 59 OHMS

R3 = 88 OHMS

R4 = 113 OHMS

V = 24 V

1) CURRENT(I1) = V/(R1+R2+R3+R4) = 24/(59+59+88+113) = 0.07523510972 AMPERES

2) CURRENT(I2) = V/(R1/R4) = 24/(59+113) = 0.13953488372093 AMPERES

3) V = I1*(R2+R3) = 0.07523510972*(59+88) = 11.05956112884 V

4) CURRENT THROUGH INDUCTOR = I2 = 0.13953488372093 AMPERES

5) CURRENT THROUGH R2 = I1 = 0.07523510972 AMPERES

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