Revision/ Ch6/ Q5

Revision/ Ch6/ Q5

  1:45 PM    Rohit

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Problem-Solving Strategy RLC Circuits The following procedure is recommended for solving series RLC circuit problems: 1.       Calculate the inductive and capacitive reactances, XL and XC. 2.       Use XL and XC together with the resistance R to calculate the impedance Z of the          circuit. 3.       Find the maximum current or maximum voltage drop with the equivalent of  Ohm’s          law, DVmax = ImaxZ. 4.       Calculate the voltage drops across the individual elements with the appropriate          variations of Ohm’s law: DVR,max = ImaxR, DVL,max = ImaxXL, and DVC,max = ImaxXC. 5.       Obtain the phase angle using tan f = (XL – XC)/R.

Q1
An AC voltage source has an output of Dv 5 (2.00 ´ 10²) sin 2pft. This source is connected to a 1.00 ´ 10² W resistor. Find the rms voltage and rms current in the resistor.

[141 V, 1.41 A]

Q2
An 8.00 mF capacitor is connected to the terminals of an AC generator with an rms voltage of 1.50 ´ 10² V and a frequency of 60.0 Hz. Find the capacitive reactance and the rms current in the circuit.

[333 W, 0.452 A]

Q3
In a purely inductive AC circuit, L = 25.0 mH and the rms voltage is 1.50 ´ 10² V. Find the inductive reactance and rms current in the circuit if the frequency is 60.0 Hz.

[9.42 W, 15.9 A]

Q4
A series RLC AC circuit has resistance R = 2.50 ´ 10² W, inductance L = 0.600 H, capacitance C = 3.50 mF, frequency f = 60.0 Hz, and maximum voltage DV_max = 1.50 ´ 10² V. Find
(a)   the impedance of the circuit,
(b)   the maximum current in the circuit,
(c)    the phase angle,
(d)   the maximum voltages across the elements, and
(e)   the average power delivered to the series RLC circuit

[588 W, 0.255 A, – 64.8^o, 63.8 V, 57.6 V, 193 V, 8.12 W]

Q5
Consider a series RLC circuit for which R = 1.50 ´ 10² V, L = 20.0 mH, DV_rms = 20.0 V, and f = 796 Hz.
(a)   Determine the value of the capacitance for which the rms current is a maximum.
(b)   Find the maximum rms current in the circuit.

[2.00 ´ 10^-6 Hz, 0.133 A]