A capacitor is connected across an ac source that has voltage amplitude 60.0 V and frequency 80.0 Hz. (a) What is the phase angle Φ for the source voltage relative to the current? Does the source voltage lag or lead the current?

Video transcript

Hi, everyone in this practice problem, we're being asked to determine the phase difference by between a current and the EMF of the power source. And also we have to determine whether the current is lagging or leading the EMF of the power source. We'll have an output of an AC power source connected to a capacitor with a frequency of 100 and 50 Hertz and an R MS voltage of 25 fold. The options given are a, the current will lead the eemf voltage by 90 degrees B. The current will lack the MF voltage by 90 degrees C. The current will lead the EMF voltage by 45 degrees. And lastly D the, the current will lack the EMF voltage by 45 degrees. So the ac current I in the circuit is going to be given by I equals to I multiplied by cosine of omega T. While the charge Q on the capacitor plate can be calculated by Q equals to B, the integral of the small I multiplied by DT which will be equal to, by substituting the I formula I multiplied by cosine of Omega T multiplied by DT. In this case, we will then get Q or solving the integral, we will then get Q to be equals to I divided by omega multiplied by sine of Omega T. The fault across the capacitor is going to equals to PC equals to one divided by C multiplied by omega multiplied by sine of omega C. The voltage across the capacitor equals the voltage of the power supply or the EMF from the expression of I and PC, we notice that the peak of capacitor voltage occur a quarter cycle. After the corresponding current peaks, we say that the current leads the voltage by 90 degrees due to this. Therefore, the phase difference or five will equals to 90 degrees between the current and the EMF of the power source and the current will lead the age. And that will be the answer to this practice problem where the phase difference five between the current and the EMF of the power source will actually lead the EMF voltage by 90 degrees. So the current leads the yamma voltage by 90 degrees. And that will correspond to option A in our answer choices. So option A will be the answer to this particular practice problem and that'll be it for this video. Thank you.