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An emf of 10 $\mathrm{V}$ is connected to a series $R C$ circuit consisting of a resistor of $2.0 \times 10^{6} \Omega$ and an initially uncharged capacitor of 3.0$\mu \mathrm{F}$ . Find the time required for the charge on the capacitor to reach 90$\%$ of its final value.

14 \mathrm{s}

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Rutgers, The State University of New Jersey

Hope College

University of Winnipeg

McMaster University

in this particular circuit, which is known as Siri's RC. So kid with the given it does you miss is 10 world resistance value is to into generous to six homes and the capacity res off three microphones. And basically, we need to find the time required for the charge on the capacitor to reach 90% sulfur final value. So now to start with this, let the charge on capacity after a certain amount of time se de seconds in our C circuit be killed groups Well, as you this monk you No. Okay. So as we move further, we need to make use of a question which is common to use. A small Q is equal to a capital Q multiplied by one minus is too minus d upon our c not here. This queue there is capital Q known as Google or begins the final charge are is the resistance and sees the capacities now asked for the given condition, sir. Right Asper The condition que becomes 90% off final value. This is a condition given So what we need to do here is therefore small que physical to 90% off capital Q. So which is 90 divided by 100 times. Q, which is equal to 0.9. Q. There's a value of this morning. Q. Now we need to repair. Is this in the main equation? Therefore, what we do here is 0.9 Q, which is equal to Q multiplied by one minus. Etess to minus T upon. Time goes, and that is our C. So therefore, solving further. 0.9 q divided by Q, which is equal to one minus eat is to minus T a partner. See here Q on Q in the monitor on the denominator, respectively, it canceled. So boring nine minus one is equal to minus ears to my nasty upon our C. Therefore minus a 0.1 is equal to mind yourself. It is to minus T upon honesty here, minus sign gets cancer from Bo decides to eat is to minus t upon. Our C is equal to 0.1. Now, as we go ahead, we get we need to apply. So write a blind natural look on The board decides so therefore, for the left hand side, we get minus t on RC When we apply natural log Do it is to x don't and natural log off point. What? So therefore my s t is equal to natural appoint. One is minus off 2.3. But Mikey Blimey, Darcy, do the right inside. So therefore minus T is equal to minus off Group 0.3. Mike, you played by. Well, you're far is giving us doing good in his 26 capital C. That is capacitor. Why lose three microphones? So to intrude eminence to minus six. Finally minus sign is getting cancer and we get value of gs 13.8 seconds. This is the answer that we were looking for. So we just write down in gay himself a statement that the time required floor the charge on capacity reach 90% off Its final value will be Turgeon 0.8 seconds or began. Say approximately 40 seconds. This would be our answer