Question

A resistor (R=9.00×102Ω), a capacitor (C=0.250μF), and an inductor (L=2.40H) are connected in series across a 2.40×10²-Hz AC source for which ΔVmax=1.15×10² V (a) Calculate the impedance of the circuit. kΩ (b) Calculate the maximum current delivered by the source. a (c) Calculate the phase angle between the current and voltage.

Answer 1

To calculate the impedance of the circuit, use the formula Z = sqrt(R^2 + (Xl - Xc)^2). The maximum current delivered by the source can be calculated using the formula Imax = Vmax/Z. The phase angle between the current and voltage can be calculated using the formula φ = arctan((Xl - Xc)/R).

Step-by-step explanation:

To calculate the impedance of the circuit, we can use the formula Z = sqrt(R^2 + (Xl - Xc)^2), where R is the resistance, Xl is the inductive reactance, and Xc is the capacitive reactance. In this case, R = 9.00 x 10^2 Ω, Xl = 2πfl, and Xc = 1/(2πfc). Plugging in the values, we get Z = sqrt((9.00 x 10^2)^2 + (2πfl - 1/(2πfc))^2).

To calculate the maximum current delivered by the source, we can use the formula Imax = Vmax/Z, where Vmax is the maximum voltage and Z is the impedance. In this case, Vmax = 1.15 x 10^2 V and Z is the value calculated in part (a).

To calculate the phase angle between the current and voltage, we can use the formula φ = arctan((Xl - Xc)/R), where Xl is the inductive reactance, Xc is the capacitive reactance, and R is the resistance. In this case, Xl = 2πfl, Xc = 1/(2πfc), and R = 9.00 x 10^2 Ω.