A 4.65-μF and an 9.30-μF capacitor are connected in series to a 60.0-Hz generator operating with an rms voltage of 111 V. What is the rms current supplied by the generator?
The capacitors are in series so I used C = C1*C2/(C1 + C2) and got C = 3.1*10^-6
Xc = 1/wC ---> Xc = 1/(60*3.1*10^-6) = 5376
Irms = V/Xc ---> 111/5376 = .021A
But this is wrong? Thanks for the help!
w=2PI*f
Xc=1/(2PI*f*C)
Thanks for your help! I see my mistake!
To find the total capacitance of the series combination, you correctly used the formula C = C1 * C2 / (C1 + C2). In this case, C1 = 4.65 μF and C2 = 9.30 μF. By plugging in the values, you should get C = 3.1 μF.
Next, you correctly calculated the capacitive reactance (Xc) using the formula Xc = 1 / (ωC), where ω is the angular frequency (2πf) and C is the total capacitance. In this case, f = 60 Hz, so ω = 2π * 60 = 376.99 rad/s. Plugging in the values, you should get Xc = 1 / (376.99 * 3.1 * 10^-6) = 871.89 Ω.
However, the mistake lies in the calculation of the rms current. The correct formula is Irms = V / Xc, where V is the rms voltage supplied by the generator. In this case, V = 111 V. Plugging in the values, you should get Irms = 111 / 871.89 = 0.127 A (rounded to three decimal places).
So, the correct rms current supplied by the generator is approximately 0.127 A.