A generator connected to an RLC series circuit has an rms voltage of 120 V and a

Question

A generator connected to an RLC series circuit has an rms voltage of 120 V and an rms current of 34 mA. (a) If the resistance in the circuit is 3.3 k and the reactive capacitance is 6.6 k, what is the inductive reactance of the circuit? (b) If generator powering the circuit drives a 60 Hz AC signal, what is the capacitance? (c) What is the inductance? (d) Find the angular frequency one would drive the generator at in order to get the strongest current to flow in the circuit (i.e. what angular frequency yields the lowest impedance).

Explanation / Answer

Here ,

Vrms = 120 V

Irms = 34 mA

R = 3.3 kOhm

Xc = 6.6 kOhm

for the inductive reactance Xl

as Z = sqrt(R^2 + (Xl - Xc)^2)

120/34 = sqrt(3.3^2 + (Xl - 6.6)^2)

solving for Xl

Xl = 7.85 kOhm , 5.35 kOhm

the inductive reactance of the circuit is 7.85 kOhm , 5.35 kOhm

b)

Now ,for the capacitance

Xc = 1/(2pi * f * C)

6600 = 1/(2pi * 60 * C)

C = 4.02 *10^-7 F

the capacitance is 4.02 *10^-7 F

c)

for the inductance

Xl =5.35 kOhn

2pi * f * L = 5.35 *10^3

2pi * 60 * L = 5.35 *10^3

L = 14.2 H

the inductance is 14.2 H

d)

for the maximum current

angular frequency = 1/sqrt(L * C)

angular frequency = 1/sqrt(4.05 *10^-7 * 14.2)

angular frequency = 417.1 rad/s

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.