Dominic and Zoey decide they are ready to try a homework problem.The AC circuit illustrated in the simulation contains an inductor with inductance L = 1.64 H and has a frequency of f = 1.37 Hz with an applied AC voltage whose maximum is ΔVmax = 2.24 V.Find the inductive reactance. ΩFind the rms current in the circuit. Your response differs from the correct answer by more than 10%. Double check your calculations. A
Question
Dominic and Zoey decide they are ready to try a homework problem.The AC circuit illustrated in the simulation contains an inductor with inductance L = 1.64 H and has a frequency of f = 1.37 Hz with an applied AC voltage whose maximum is ΔVmax = 2.24 V.Find the inductive reactance. ΩFind the rms current in the circuit. Your response differs from the correct answer by more than 10%. Double check your calculations. A
Solution
To find the inductive reactance (X_L), we can use the formula:
X_L = 2πfL
where: f = frequency = 1.37 Hz L = inductance = 1.64 H
Substituting these values into the formula, we get:
X_L = 2π * 1.37 Hz * 1.64 H = 14.14 Ω
Next, to find the rms current (I_rms) in the circuit, we can use Ohm's law:
I_rms = ΔV_rms / X_L
The rms voltage (ΔV_rms) is given by ΔV_max / sqrt(2), where ΔV_max = 2.24 V. So,
ΔV_rms = 2.24 V / sqrt(2) = 1.58 V
Substituting these values into Ohm's law, we get:
I_rms = 1.58 V / 14.14 Ω = 0.112 A or 112 mA
So, the inductive reactance is 14.14 Ω and the rms current in the circuit is 112 mA.
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