An emf source with ε = 120V, a resistor with R = 80.0Ω, and a capacitor with C = 4.00 μF are connected in series. As the capacitor charges, when the current in the resistor is 0.900 A, what is the magnitude of the charge on each plate of the capacitor?

Video transcript

Welcome back, everybody. We are taking a look at this circuit right here and we are told at time T or after a time T when the switch is closed, we're told that the AM meter down here reads 0.5 amps. And we are tasked with finding what is going to be the charge across the capacitor at that time. T Well, we know that the charge is just going to be equal to the capacitance times the voltage across the capacitor. But what is the voltage across the capacitor? Well, we're going to use uh loop rule that states that the voltage across everything is going to have to be equal to zero. So what we can go ahead and do here is I'm gonna subtract VB from both sides at VR to both sides. And we get that VC is equal to V B minus V R. We have V B. That's just the voltage of the battery right here. I'm gonna label this as having a voltage across the capacitor and the voltage across the resistor. We don't know the voltage across the resistor. Well, we have another simple formula for this, the voltage across the resistor is just the resistance times the current. And the current that we're gonna be using is the reading on the meter. So let's go ahead and plug in some values here. We have that the resistance is 60 OEMs. I'm 0.5 amps giving us three volts gonna change color here as we're gonna be working our way back up these formulas. So now we have that VC is equal to V B minus V R. We have the voltage of the battery is nine minus the voltage across the resistor is three, giving us a voltage of six volts. Now, we can go ahead and calculate the charge across the capacitor that's just equal to the capacity of 100 micro fare adds. But we need it in fair ads. So I'm gonna multiply it by 10 to the negative six times the voltage across R capacitor which is six, giving us a final answer of 600 micro columns corresponding to our answer. Choice of C. Thank you all so much for watching. Hope this for your help. We will see you all in the next one.