Question

An RLC series circuit has R=100 ohms, C=25mF, and L=0.16H. (A) Given that the frequency of the voltage source is 5OH, find the impedance and the phase angle? (B)For what angular frequency of an ac voltage is the current flow maximum?

Answer 1

The impedance of the RLC series circuit is approximately 100.08 ohms with a phase angle of approximately 0.31 degrees. The angular frequency of the AC voltage when the current flow is maximum is approximately 10 Hz.

Step-by-step explanation:

In an RLC series circuit, the impedance (Z) can be calculated using the formula:

Z = √(R^2 + (Xl - Xc)^2)

Given R = 100 ohms, C = 25mF, and L = 0.16H, calculate the inductive reactance (Xl) and the capacitive reactance (Xc).

The inductive reactance (Xl) can be calculated using the formula:

Xl = 2πfL

Substituting the given values, we have:

Xl = 2π(5)(0.16) = 1.6 ohms

The capacitive reactance (Xc) can be calculated using the formula:

Xc = 1/(2πfC)

Substituting the given values, we have:

Xc = 1/(2π(5)(0.025)) = 1.27 ohms

Now,calculate the impedance (Z) using the formula:

Z = √(100^2 + (1.6 - 1.27)^2) = 100.08 ohms

The phase angle (θ) can be determined using the formula:

θ = tan^(-1)((Xl - Xc)/R)

Substituting the calculated values, we have:

θ = tan^(-1)((1.6 - 1.27)/100) = 0.31 degrees

(A) The impedance of the RLC series circuit is approximately 100.08 ohms and the phase angle is approximately 0.31 degrees.

To determine the angular frequency (ω) when the current flow is maximum, we need to find the resonant frequency (fr) of the circuit. The resonant frequency can be calculated using the formula:

fr = 1/(2π√(LC))

Substituting the given values, we have:

fr = 1/(2π√(0.16(0.025))) = 10 Hz

(B) The angular frequency of the AC voltage when the current flow is maximum is approximately 10 Hz.