Question

A series RLC circuit has a capacitance mC=121μF, an inductance L=114mH, and is driven by an AC generator producing a root-mean-square (rms) voltage Vrms​=100.0V with a frequency f=90.0Hz. What resistance R is necessary to produce an rms current 1.20A?

Answer 1

A series RLC circuit has a capacitance mC=121μF, the resistance R necessary to produce an rms current of 1.20A in an RLC series circuit is 83.3 Ω.

Step-by-step explanation:

In an RLC circuit, the impedance (Z) is given by the formula:

Z = √(R^2 + (XL - XC)^2)

Where

R is the resistance

XL is the inductive reactance,

XC is the capacitive reactance.

The reactances can be calculated using the formulas:

XL = 2πfL and XC = 1/(2πfC).

In this case, the given frequency f is 90.0 Hz and the capacitance C is 121μF, so XC = 1/(2π(90.0)(121×10-6)).

The impedance Z can be used to find the resistance R using the formula:

R = Vrms/Irms, where Vrms is the root-mean-square voltage and Irms is the root-mean-square current.

Substituting the given values, we have:

R = (100.0)/(1.20) = 83.3 Ω.

So therefore the resistance R is necessary to produce an rms current 1.20A is 83.3 Ω.