Laboratory experiments with series RLC circuits require some care, as these circ
ID: 2010416 • Letter: L
Question
Laboratory experiments with series RLC circuits require some care, as these circuits can produce large voltages at resonance. Suppose you have a 1.00-H inductor (not difficult to obtain) and a variety of resistors and capacitors. Design a series RLC circuit that will resonate at a frequency (not an angular frequency) of 60.0 Hz and will produce at resonance a magnification of the voltage across the capacitor or the inductor by a factor of 17.1 times the input voltage or the voltage across the resistor.a) What is the capacitance required for this circuit?
b) And what is the resistance required for this circuit?
Explanation / Answer
Given inductance of the inductor L = 1 H series RLC circuit that will resonate at a frequency of 60.0 Hz at resonance frequency inductive reactance ( XL ) = capacitive reactance ( X C ) so the impedance of the circuit is Z = R voltage across inductor is V L = I XL 17.1 V = ( V / R ) ( 2f L ) resistance of the resistor R = 2f L / 17.1 = 2 *60* 1 / 17.1 = 22.0469 voltage across capacitro is V C = I X C 17.1 V = ( V / R ) ( 1 / 2 f C ) C = 1 / 2 f R (17.1) = 1 / ( 2)(60)(22.0469)(17.1) = 7.03 F =Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.