A series ac circuit consists of a voltage source of frequency 60 Hz and source voltage amplitude 345 volts, a 701-Q resistor, a 1.6 - uF capacitor, and an inductor of inductance L.(a) What must be the value of L for the phase angle to be zero? (b) When L has the value calculated in part (a), what is the current amplitude in the circuit?
Question
A series ac circuit consists of a voltage source of frequency 60 Hz and source voltage amplitude 345 volts, a 701-Q resistor, a 1.6 - uF capacitor, and an inductor of inductance L.(a) What must be the value of L for the phase angle to be zero? (b) When L has the value calculated in part (a), what is the current amplitude in the circuit?
Solution
(a) For the phase angle to be zero in a series AC circuit, the inductive reactance (XL) must be equal to the capacitive reactance (XC).
The formula for capacitive reactance is XC = 1/(2πfC), where f is the frequency and C is the capacitance.
Substituting the given values, we get XC = 1/(2π60Hz1.6μF) = 1,663.5 Ohms.
Since XL must be equal to XC for the phase angle to be zero, XL = 1,663.5 Ohms.
The formula for inductive reactance is XL = 2πfL, where L is the inductance.
Rearranging this formula to solve for L, we get L = XL/(2πf).
Substituting the known values, we get L = 1,663.5 Ohms / (2π*60Hz) = 0.44 H.
So, the value of L for the phase angle to be zero is 0.44 H.
(b) When L has the value calculated in part (a), the total impedance (Z) of the circuit is equal to the resistance (R), since the inductive and capacitive reactances cancel each other out.
So, Z = R = 701 Ohms.
The formula for the current amplitude (I) in an AC circuit is I = V/Z, where V is the voltage amplitude.
Substituting the known values, we get I = 345 volts / 701 Ohms = 0.49 A.
So, the current amplitude in the circuit is 0.49 A.
Similar Questions
A series RLC circuit has a capacitor with a capacitance of 18.0 μF , an inductor with an inductance of 1.40 H and a resistor with a resistance of 105 Ω. The circuit has a rms current of 7.50 A when the frequency is 64.0 Hz. What is the phase angle?
If the voltage in the circuit is maintained by an AC source operating at f = 60.0 Hz and the resonant frequency of the circuit is f0 = 90.0 Hz, what are the values of C (in µF) and L (in mH) in the circuit?
An LCR series circuit of capacitance 62.5 nF and resistance of 50 Ω, is connected to an A.C. source of frequency 2.0 kHz. For maximum value of amplitude of current in circuit, the value of inductance is ____mH.(Take π2=10)
The phase constant, φφ , between the voltage and the current in an AC series RLC circuit depends on multiple choicethe resistance, the capacitive reactance, and the inductive reactance.the resistance and the capacitive reactance.the resistance and the inductive reactance.the capacitive reactance and the inductive reactance.only the resistance.only the capacitive reactance.only the inductive reactance.
In a certain series RLC circuit, Irms = 9.00 A, ΔVrms = 245 V, and the current leads the voltage by 30.0°.(a)What is the total resistance (in Ω) of the circuit? Ω(b)Calculate the reactance (in Ω) of the circuit (XL − XC). Ω(c)What If? If the voltage in the circuit is maintained by an AC source operating at f = 60.0 Hz and the resonant frequency of the circuit is f0 = 90.0 Hz, what are the values of C (in µF) and L (in mH) 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.