A capacitor is connected across an ac source that has voltage amplitude 60.0 V and frequency 80.0 Hz. (b) What is the capacitance C of the capacitor if the current amplitude is 5.30 A?

Video transcript

Welcome back, everybody. We are observing a circuit with an alternating current power supply. We are told that the RMS voltage is 20 volts and we are told that it has a frequency of 18 Hertz. We are also told that the R M S current is equal to 200 million amps. And we are tasked with finding what the capacitance is. The capacitance is of the parallel plate capacitor. So let's see here. We actually have a formula that states that the capacitive reactant is equal to one over little see omega this is equal to one over the capacitance times two pi times the frequency. So I'm gonna go ahead and multiply both sides by sea over X C and we will be able to isolate our capacitance term on the left hand side here on the right, this C will cancel out and we are left with that, our capacity is equal to one over the capacitive reactant is times two pi times R frequency. But what is the capacity of reactant we have that the capacity of reactant is equal to our RMS our over our R M S current. So we know these numbers. So let's go ahead and plug in our values. We have 1 20 divided by mil amps, which is 200 times 10 to the negative third. And when we divide this, we get that our capacitive reactant is omegas great. Now that we have that we are ready to confine, find our capacities. So this is equal to one over times two pi times 60 which when we plug into our calculator gives us a final answer of 4.42 times 10 to the negative six fair adds corresponding to our answer. Choice of a. Thank you all so much for watching. Hope this video helped. We will see you all in the next one.