Riley and Wyatt now do a homework problem.The AC circuit illustrated in the simulation contains a capacitor with a rather large capacitance C = 3.95 F, ΔVmax = 2.60 V, and has a frequency of 2.20 Hz.Find the capacitive reactance XC. ΩFind the rms current in the circuit.
Question
Riley and Wyatt now do a homework problem.The AC circuit illustrated in the simulation contains a capacitor with a rather large capacitance C = 3.95 F, ΔVmax = 2.60 V, and has a frequency of 2.20 Hz.Find the capacitive reactance XC. ΩFind the rms current in the circuit.
Solution
To find the capacitive reactance (Xc), we can use the formula:
Xc = 1 / (2 * π * f * C)
where:
- f is the frequency, which is 2.20 Hz
- C is the capacitance, which is 3.95 F
Substituting the given values into the formula, we get:
Xc = 1 / (2 * π * 2.20 Hz * 3.95 F) = 0.018 Ω
Next, to find the rms current (Irms) in the circuit, we can use Ohm's law, which states that I = V / R. In this case, the resistance is the reactance Xc, and V is the rms voltage, which is ΔVmax / √2.
So, Irms = ΔVmax / (Xc * √2) = 2.60 V / (0.018 Ω * √2) = 103.3 A.
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