circuit_with_two_resistors_and_one_capacitor

circuit_with_two_resistors_and_one_capacitor - 1 1 1 1 R V...

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Circuit with Two Resistors and One Capacitor Given: v F i n d : 8 V ? 0 Q 43 1 R ? 0 . 1 I ? 0 . 2 70 2 R I F C 11 ? 1 I ? 2 I ? Q ? . 1 T I ? . 2 T I ? Initially, the capacitor is uncharged, and the switch is open. At t = 0, the switch is closed. The positive directions of the currents are represented by arrows in the diagram. (a) Calculate the charge on the positive plate of the capacitor just after the switch is closed. (b) Calculate the following currents immediately after the switch is closed. (c) After the switch has been closed for a long time, calculate the following quantities. (d) At some yet later time T , the switch is again opened. Calculate the following currents immediately afterward. (e) What is the time constant of the discharging circuit? Solutions a.) To find we can use the following formula: 0 Q 0 0 Q b.) To find & we can use the following formula: 0 . 1 I 0 . 2 I we need to loop equations and one current equation 3 2 1 I I I 0 1 1 2 2 I R I R V since 1 1 I R V V c 0 0 Q 0 C Q V c 0 1 1 I R V
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We get V I R
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Unformatted text preview: 1 1 1 1 R V I 1 1 2 2 I R I R V 2 2 V I R V 2 2 I R 2 I c.) To find , & Q we can use the following formula: 1 I 2 I after a long time the capacitor is fully charged and 3 I I R R V 2 1 they are in series 2 1 I I I 2 1 2 1 I I R R V I 2 1 2 1 R R V I I Since and C are in parallel 2 R c V V 2 2 1 2 2 2 2 R R V R I R V 2 1 2 R R V CR CV Q c 2 1 2 R R CVR Q d.) To find & we can use the following formula: T I . 1 T I . 3 no closed loop . 1 T I 2 1 2 2 1 2 2 . 3 R R V R R R V R R V I c T minus sign because the top plate is positive i.e. current moves the other way 2 1 . 3 R R V I T e.) To find we can use the following formula: C R RC 2 C R 2...
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circuit_with_two_resistors_and_one_capacitor - 1 1 1 1 R V...

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