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A $500-\Omega$ resistor, an uncharged $1.50-\mu \mathrm{F}$ capacitor, and a 6.16 -V emf are connected in series. (a) What is the initial current? (b) What is the $R C$ time constant? (c) What is the current after one time constant? (d) What is the voltage on the capacitor after one time constant?
a) $\cdot 012$b) 75 seec) 004 Ampd) 3$\cdot 89 c$
Physics 102 Electricity and Magnetism
Chapter 21
Circuits, Bioelectricity, and DC Instruments
Direct-Current Circuits
Cornell University
Rutgers, The State University of New Jersey
University of Sheffield
University of Winnipeg
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So in this problem, we, uh, connect the the battery with the resistance and ah, condition with the pastor here. So this is a v e r n a c. So, in part A, we want to know the initial current. So for it, we so for the initial current. Ah, because this is a charging process, right? So the initial currents and people too. Ah, the V divide by our it's just just like we just ignore the sea. So the video is Ah, dear. 0.123 amperes. And in part B, the time constant hole. It's defined as our time seat. Right? So we put in the very for the resistance and the capacities and exceeded the it's 7.5 times 10 to the negative force seconds. And in Percy, suppose, uh, the time has possible one time constant. And we want to know the current and a moment. So that means t equal tall. So the current expression is ah, equal. I notes times e negative T or tall. Right? So I know it is the one that we found here, and it decays exponentially on, uh so, uh, we already know that t were teased Hall so we can plug into values, Will I not? And t so we can see that the video is ah, 4.53 times 10 to the negative third and peers and in part D. Ah, We want to know the the devoted, your cross the cross there after one time after one time constant. So we have the equal the notes one minus e to the negative t over tall. Great. Because so because, uh, if the time has ah, if the time is very large, it's like a long time has passed. Then we should get the body across the capacitor equal to the e m f right, And right here the V not simply equal to ah, the the E m f. So we can plug in the video for the V notes, which is Ah, 6.16 bolts and a one minus c. It's extra native want. Right, So we come to in the video is ah, three point 89 lots. Okay,
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