# Physics

posted by .

A series RCL circuit has a resonant frequency of 1500 Hz. When operating at a frequency other than 1500 Hz, the circuit has a capacitive reactance of 5.0 Ù and an inductive reactance of 30.0 Ù. What are the values of (a) L and (b) C?

I know I should be using these 2 equations:
Xc= 1/(2*pi*f*C)
Xl= 2*pi*f*L

Since each have 2*pi*f in them, with rearranging and substituting, you get:

C= L/(Xl*Xc)

However, with this it leaves the 2 unknowns, and I'm not sure what other equations I could use?

• Physics -

f=1500 Hz, X(C)=5Ω, X(L)=30 Ω

X(C)= 1/ωC,…..(1)
X(L)=ωL, ……..(2)
Multiply (1) by (2):
X(C) •X(L)= ωL/ ωC =L/C.
C=L/X(C) •X(L) …..(3)
Resonant frequency is
f=1/2π√(LC) =>
C=1/4•π²•f²•L ….(4)
Equate (3) and (4)
L/X(C) •X(L) =1/4•π²•f²•L,
L=sqrt{X(C) •X(L}/2•π•f=
=sqrt(5•30)/2π•1500=1.3•10^-3 H=
=1.3 mH,
C= L/X(C) •X(L)=
=1.3•10^-3/5•30=8.67•10^-6 =F=
= 8.67 μF

## Similar Questions

1. ### physics

the table below shows the values of the resistance, capcitive reactance and inductive reactance for five RCL circuits. in which circuit will the voltage lead the current?
2. ### physics

The phase angle of an RLC series circuit with an inductive reactance of 200 Ù and a capacitive reactance of 100 Ù is 40.0°. What is the value of the resistor in this circuit?
3. ### Physics

The capacitance in a series RCL circuit is C1 = 1.2 μF, and the corresponding resonant frequency is f01 = 7.2 kHz. The generator frequency is 1.2 kHz. What is the value of the capacitance C2 that should be added to the circuit …
4. ### Physics

In a series RCL circuit the generator is set to a frequency that is not the resonant frequency. This nonresonant frequency is such that the ratio of the inductive reactance to the capacitive reactance of the circuit is observed to …
5. ### Physics- Circuits

In a series RCL circuit the generator is set to a frequency that is not the resonant frequency. This nonresonant frequency is such that the ratio of the inductive reactance to the capacitive reactance of the circuit is observed to …
6. ### PHYSICS

In a series RCL circuit the generator is set to a frequency that is not the resonant frequency. This nonresonant frequency is such that the ratio of the inductive reactance to the capacitive reactance of the circuit is observed to …
7. ### Physics

A series RCL circuit has a resonant frequency of 1530 Hz. When operating at a frequency other than 1530 Hz, the circuit has a capacitive reactance of 5.0 Ω and an inductive reactance of 33.0 Ω. What is the value of L?
8. ### Physics

A series RCL circuit has a resonant frequency of 1470 Hz. When operating at a frequency other than 1470 Hz, the circuit has a capacitive reactance of 5.0 Ù and an inductive reactance of 29.0 Ù. (a) What is the value of L?
9. ### Physics

A 50 ohm resistor is connected in series with a 0.2 H inductor, a 40 microFarad capacitor, and an AC Generator yielding 120 v (RMS) at 60 Hz. Find A) the inductive reactance b) the capacitive reactance and c) the total reactance, the …
10. ### College Physics

At what frequency does the inductive reactance of a 42.0 µH inductor equal the capacitive reactance of a 42.0 µF capacitor?

More Similar Questions