An AC circuit has an emf of 15.0cos(wt) V. There is also a 330. Ω resistor, a 5.10 nF capacitor a 0.0840 H inductor in the circuit. What is the value of the reactances XC and XL if the emf frequency is 2.30 kHz? XC = 1.36×104 Ω and XL = 1.21×103 Ω XC = 3.41×105 Ω and XL = 773 Ω XC = 2.71×104 Ω and XL = 2.43×103 Ω XC = 8.53×104 Ω and XL = 193 Ω
Question
An AC circuit has an emf of 15.0cos(wt) V. There is also a 330. Ω resistor, a 5.10 nF capacitor a 0.0840 H inductor in the circuit. What is the value of the reactances XC and XL if the emf frequency is 2.30 kHz? XC = 1.36×104 Ω and XL = 1.21×103 Ω XC = 3.41×105 Ω and XL = 773 Ω XC = 2.71×104 Ω and XL = 2.43×103 Ω XC = 8.53×104 Ω and XL = 193 Ω
Solution
The reactance of a capacitor (Xc) and an inductor (XL) can be calculated using the following formulas:
Xc = 1/(2πfC) XL = 2πfL
where: f is the frequency, C is the capacitance, and L is the inductance.
Given: f = 2.30 kHz = 2300 Hz (since 1 kHz = 1000 Hz), C = 5.10 nF = 5.10 x 10^-9 F (since 1 nF = 10^-9 F), and L = 0.0840 H,
we can substitute these values into the formulas to find Xc and XL.
Xc = 1/(2π(2300)(5.10 x 10^-9)) ≈ 1.36 x 10^4 Ω XL = 2π(2300)(0.0840) ≈ 1.21 x 10^3 Ω
So, the reactances Xc and XL are approximately 1.36 x 10^4 Ω and 1.21 x 10^3 Ω, respectively.
Similar Questions
An AC circuit has a voltage source 5.00cos(wt) V. There is also a 180. Ω resistor and a 2.70 nF capacitor in the circuit. What is the value of the peak voltages VR and VC if the emf frequency is 4.10 kHz?
An inductor with inductance L is connected to an AC power source having a peak value of 37.5 V and f = 911 Hz. If the reactance of the inductor is supposed to be 239.83 Ω, what value of L is needed? mH
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
A capacitor with capacitance C = 4.29 ⋅ 10−6 F𝐶 = 4.29 · 10-6 F is connected to an AC power source having a peak value of 14.1 V and f = 151 Hz. Find the reactance of the capacitor. Ω Calculate the maximum current in the circuit. A
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.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.