Question

An RLC circuit is used in a radio to tune into the radio lagos fm Station broadcasting at 93.5Hz. The resistance is 15ohms and the inductance is 1.6 H. Calculate the capacitance used​

Answer 1

The characteristics of the RLC circuit allow to find the result for the capacitance at a resonance of 93.5 Hz is:

• Capacitance is C = 1.8 10⁻⁶ F

A series RLC circuit reaches the maximum signal for a specific frequency, called the resonance frequency, this value depends on the impedance of the circuit.

            $Z^2 = R^2 + ( wL - \frac{1}{wC} )^2$  

Where Z is the impedance of the circuit, R the resistance, L the inductance, C the capacitance and w the angular velocity. The negative sign is due to the fact that the current in the capacitor and the inductor are out of phase.

In the case of resonance, the impedance term completes the circuit as a resistive system.

           $wL - \frac{1}{wC} = 0 \\w^2 = \frac{1}{LC}$  

           

Indicate that the inductance L = 1.6 H and the frequency f = 93.5 Hz.

Angular velocity and frequency are related.

         

         w = 2π f

           

Let's  substitute.

          $C = \frac{1}{L ( 2 \pi f)^2 }$  

 

Let's calculate.

         $C = \frac{1}{1.6 \ ( 2\pi \ 93.5)^2}$  

         C = 1.8 10⁻⁶ F

In conclusion with the characteristics of the RLC circuits we can find the result for the capacitance at a 93.5 Hz resonance is:

• Capacitance is C = 1.8 10⁻⁶ F

Learn more about serial RLC circuits here: brainly.com/question/15595203