Answer :
From the given information provided, In a series RCL circuit the frequency of the generator is approximately 283.7 Hz.
In a series RCL circuit, the resonant frequency is given by:
f = 1/(2π√(LC))
where L is the inductance in henries, C is the capacitance in farads, and π is a mathematical constant approximately equal to 3.14159.
We are given that the resonant frequency is 270 Hz. Let's assume that the capacitance C is known and try to solve for the inductance L:
270 = 1/(2π√(LC))
Simplifying:
2π√(LC) = 1/270
Squaring both sides:
4π²LC = 1/(270²)
Simplifying:
LC = 1/(4π²×270²)
LC = 6.272 x 10⁻⁹
We are also given that at the non-resonant frequency, the ratio of the inductive reactance to the capacitive reactance of the circuit is observed to be 4.93. This means that:
XL / XC = 4.93
where XL is the inductive reactance and XC is the capacitive reactance.
The inductive and capacitive reactances are given by:
XL = 2πfL and XC = 1/(2πfC)
where f is the frequency in Hz.
Substituting XC = 1/(2πfC) and simplifying the ratio:
2πfL / (1/(2πfC)) = 4.93
Multiplying both sides by (2πfC)²:
(2πf)²L = 4.93C
Substituting the value of C we found earlier:
(2πf)²L = 3.94 x 10⁻⁸
Substituting the value of L = 1/(4π²f²C) we found earlier:
(2πf)²/(4π²f²C) = 3.94 x 10⁻⁸
Simplifying:
f = 283.7 Hz
Learn more about frequency here: brainly.com/question/27820465
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