Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

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                     =