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Problem 34 Hard Difficulty

An uncharged capacitor and a resistor are connected in series to a source of emf. If $\boldsymbol{E}=9.00 \mathrm{V}, C=20.0 \mu \mathrm{F},$ and $R=1.00 \times$ $10^{2} \Omega,$ find (a) the time constant of the circuit, (b) the maximum charge on the capacitor, and (c) the charge on the capacitor after one time constant.

Answer

a. t a u=0.002 \mathrm{sec}
b. Q=1.8 \times 10^{-4} \mathrm{coulombs}
c. q=1.14 \times 10^{-4} \mathrm{coulombs}

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Video Transcript

ask for the given. Dido. There is a charge capacity. We're just gonna get in CDs with the register and the battery they respect. Your values are reading. No, we need to find the time constant off the circuit. So basically, we're right here. The time constant off the circuit is denoted as tower. There's this symbol so therefore toe is the product of register and the capacitor, so that's right. The values return given are is a good 200 homes, and the capacity venue is even as 20 microfiber. So there's 20 in group tenderness to minus six. Friends, therefore, for the calculation will be tall with sick or two 2000 including these two minus six, which is equal to do to into then is two minus three seconds. Because now that it's time, constant is major in second. So therefore we're right. The time constant off the circuit is two milli seconds and report this in bracket. That is the answer to the step, eh? No, let's see the step be. We need to find the maximum charge and the capacity so we just write down that is willing to find maximum charge on capacity that is what we need to find out. Now we'll make the use off this equation that is Q is equal to see Multiplied by in if now here You sense for the charge and grooms were right down charge in columns Here, C stands for the capacities which is a major defeat for ads on DDE B stands for E A myth that is major Woods. So we need to understand that. So when we may, even though I didn't know if you want with enough of the battery will write down men you miss off battery is equal two the potential difference. The charge on the capacitor will be maximum So therefore, in order to can create que max, that is maximum charge in the capacity will make use off this equation which we already written Easy Quito Charge And the capacitor is no better camp out the capacitance. So it is 20 Microsort, $22 from minus six multiplied by back. You will just that his 19 wards. So finally we get the value s 1 80 indigenous to minus six groups. So right now And that would be around Sir, that is maximum charge on capacity is 1 80 micro clubs and this will be our final answer for the step would be, Let's talk about next year step. See, we need to find charge and the capacitor after one time constant. So in order to do that, we make use off this equation. All right, on the question that is, we need to find charge on capacity after one time constant. And the equation for this will be small. Keel is equal to maximum charge multiplied by the equation off one minus is too minus D upon toe here, as you already know that, how is the time constant now, since the question is, we need to find the charge in the capacitor after one time constant, we need to substitute so substituting Dow for okay, that is a condition. So Q is equal to que Max a Jew. One minus. It is too minus toe a point. So this becomes one. Ultimately secure max multiplied by one minus. It is to minus one. And when we use calculated to government, is we get the value off this bracket a 0.6 tree, too. Therefore, Q is equipped to 0.63 times you, Max. This is what we can right in the form of equation. Now let's substitute the value of Q Max as 1 18 micrograms, too. Now substitute value off Cue Max as 1 80 into tennis to minus six columns in this equation. What would get here as Q. Is 1/4 to 0.63 in ju 1 80 include entities to minus six. So we're just coming as 113.4 include tennis. You minus six columns. Should this you have a good dancer. That charge on the capacity elf girl one time constant will be 113 born, four intrude eminence to minus six columns. This is our final answer.

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