In a circuit, we can connect resistors and capacitors together in series or para
ID: 1790057 • Letter: I
Question
In a circuit, we can connect resistors and capacitors together in series or parallel. Although we can combine resistors that are in series or parallel into a single total resistor, there is no way to combine resistors with capacitors together into a single object when they are in AV,att series or parallel. Resistors and capacitors operate very differently in a circuit, and connecting them together causes circuits to exhibit more complicated behavior. We can still study these circuits using Kirchhoff's 1. iples, however, as we will see in this problem. We'lluse the circuit shown here in which a resistor, capacitor, switch, and battery are connected in series. We begin with the switch open and the capacitor uncharged (IQI-0) When the switch is closed (so it is like an ordinary wire), write an equation that relates the potent a. difference of the battery lAV batel to the potential differences across the resistor lAVel and the capacitor AVel Use lavbatt|-8 V, R = 50 , and C 0.12 F for the following questions. b. At the instant the switch is closed, current is flowing but no charge has built up on the capacitor plate Determine the following: ili. The current in the circuit As time passes, state whether the following quantities increase, decrease, or stay the same. Explain your reasoning. c. i. 1QExplanation / Answer
from kirchoff's principle
dVbatt - dVR - dVc = 0
dVbatt - i*R - dq/C = 0
dVbatt - (dq/dt)*r - dq/c = 0
solving for q
q = (dvbatt*C)*(1 - e^-(t/RC))
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b)
dVc = 0
ii)
dVR = 8 V
iii)
i = dVbatt/R = 8/50 = 0.16 A
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c)
(i)
as time passes charge increases and becomes maximum after long time
Q = dVbatt*C
ii)
dVc increases and becomes maximum dVc = Vbatt