A series circuit contains a 115-Ω resistor, a 0.573-H inductor, a 0.417-μF capacitor, and a time-varying source of emf providing 43.9 V. (a) What is the resonant angular frequency of the circuit? rad/s (b) What current will flow through the circuit at the resonant frequency? A
Question
A series circuit contains a 115-Ω resistor, a 0.573-H inductor, a 0.417-μF capacitor, and a time-varying source of emf providing 43.9 V. (a) What is the resonant angular frequency of the circuit? rad/s (b) What current will flow through the circuit at the resonant frequency? A
Solution
(a) The resonant angular frequency (ω) of a series RLC circuit is given by the formula:
ω = 1 / √(LC)
where L is the inductance and C is the capacitance.
First, we need to convert the capacitance from μF to F.
1 μF = 1 x 10^-6 F
So, C = 0.417 x 10^-6 F
Now, we can substitute the values into the formula:
ω = 1 / √((0.573 H) * (0.417 x 10^-6 F)) = 1 / √(2.39 x 10^-7) = 2048.1 rad/s
(b) The current (I) in a series RLC circuit at resonance is given by the formula:
I = V / R
where V is the voltage and R is the resistance.
Substituting the given values into the formula:
I = 43.9 V / 115 Ω = 0.381 A
So, the resonant angular frequency of the circuit is 2048.1 rad/s and the current that will flow through the circuit at the resonant frequency is 0.381 A.
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