The capacitance in a series RLC circuit is [tex]C_1 = 2.6 \, \mu F[/tex], and the corresponding resonant frequency is [tex]f_{01} = 7.1 \, kHz[/tex]. The generator frequency is [tex]3.2 \, kHz[/tex]. What is the value of the capacitance [tex]C_2[/tex] that should be added to the circuit so that the circuit will have a resonant frequency that matches the generator frequency?

The capacitance C₂ to be added to the RCL circuit can be calculated using the resonant frequency formula and rearranging it to solve for C₂. This is done assuming that the circuit's inductance remains constant, and using the given values for the original capacitance (C₁), the initial resonant frequency (f₀₁), and the generator's frequency (f₀₂).

Explanation:

This question is about finding the value of capacitance C₂ that should be added to a series RCL circuit to match the resonant frequency to the generator frequency. The resonant frequency (fo) of a series RCL circuit is calculated using the formula: fo = 1/(2π√LC)

where L is the inductance and C is the capacitance. Since we are looking for the new capacitance (C₂) that will match the circuit's resonant frequency to the generator's, we can rearrange the formula to solve for C₂, giving us: C₂ = 1/((2πf₀₂)² L) - C₁ Here, f₀₂ is the generator frequency. Using the given values, and assuming that the inductance (L) remains constant when we add the new capacitance, we can calculate the value of C₂.

Learn more about Series RCL Circuits here:

https://brainly.com/question/31882184

#SPJ11