00:01
For this problem on the topic of alternating currents, we are told that an ac generator with emf amplitude 220 volts and operating at a frequency of 400 hertz causes oscillations in a series rlc circuit, which has resistance, inductance and capacitance, 220 oms, 150 millie henries, and 24 micropharas, respectively.
00:23
We want to find the capacitor reactants, the impedance said, the current amplitude, and we are then told.
00:30
That a second capacitor of the same capacitance is connected in series with the other components, and we want to find whether the values of xe, z, and i decrease, increase, or remain the same.
00:43
Now the capacitive reactants xc is equal to 1 over 2 pi fc and these values are known so we can calculate this capacitor reactants.
00:59
This is one divided.
01:02
By 2 pi times the frequency of oscillations 400 hertz times the capacitance 24 times 10 to the minus 6 ferrets and so we get the capacitor reactants to be 16 .6 oms next for part b the impedance z is the square root of the resistance r squared plus xl minus xc all squared, which is the square root of r squared plus 2 pi fl minus xc all squared.
02:00
And so again, if we substitute our values into this, we get this to be the square root of 220 oms squared times 400 hertz times the inductance of 150 times 10 to the minus 3 henries minus 16 .6 oms all squared and so we get the impedance z to be 422 oms...