Figure 27-67 displays two circuits with a charged capacitor that is to be discha
ID: 2153201 • Letter: F
Question
Figure 27-67 displays two circuits with a charged capacitor that is to be discharged through a resistor when a switch is closed. In figure (a) below, R1 = 22.3 ? and C1 = 5.06 ?F. In figure (b) below, R2 = 10.7 ? and C2 = 8.17 ?F. The ratio of the initial charges on the two capacitors is q02/q01 = 1.68. At time t = 0, both switches are closed. At what time t (in ms) do the two capacitors have the same charge?
Number
Figure 27-67 displays two circuits with a charged capacitor that is to be discharged through a resistor when a switch is closed. In figure (a) below, R1 = 22.3 ? and C1 = 5.06 ?F. In figure (b) below, R2 = 10.7 ? and C2 = 8.17 ?F. The ratio of the initial charges on the two capacitors is q02/q01 = 1.68. At time t = 0, both switches are closed. At what time t (in ms) do the two capacitors have the same charge? Number Units msExplanation / Answer
q= q(max)[1-e^(-t/RC)] q1 = q2 at t time qmax1/qmax2=1.68 for first capacitor q= qmax1[1-e^(-t/RC)]...1 considering r in ohms and c in microfarad get RC from given data and put in equation similarly for second to0 q=qmax2[1-e^(-t/RC)]....2 and divide equation 1 by equation 2 since q1=q2=q at time t and qmax1/qmax2 is known we 1-e^-t/(10.7*8.17)= 1.68-1.68* e^-t(22.3*5.06) t value from solving this get units to get answer
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