Resonant Frequency in Parallel CIRCUITS

Calculating Resonant Frequencies in Parallel RLC Circuits

The resonant frequency of a parallel RLC circuit is crucial for understanding how the circuit responds to different frequencies. This frequency depends on the values of resistance (R), inductance (L), and capacitance (C) in the circuit.

Formula for Resonant Frequency

The resonant frequency (f) of a parallel RLC circuit is given by:

f = 1 / (2π√(LC))

where:

• • L is the inductance in henrys (H)

  • C is the capacitance in farads (F)

  • π is Pi, approximately 3.14159
    
    

Examples of Resonant Frequencies in Parallel RLC Circuits

1. R = 4.7 kilohms, L = 1 microhenry, C = 10 picofarads

   • L = 1 × 10^-6 H

   • C = 10 × 10^-12 F

   • f = 1 / (2π√(1 × 10^-6 × 10 × 10^-12))

   • f ≈ 50.3 MHz
     
     

2. R = 4.7 kilohms, L = 2 microhenrys, C = 15 picofarads

   • L = 2 × 10^-6 H

   • C = 15 × 10^-12 F

   • f = 1 / (2π√(2 × 10^-6 × 15 × 10^-12))

   • f ≈ 29.1 MHz
     
     

3. R = 4.7 kilohms, L = 5 microhenrys, C = 9 picofarads

   • L = 5 × 10^-6 H

   • C = 9 × 10^-12 F

   • f = 1 / (2π√(5 × 10^-6 × 9 × 10^-12))

   • f ≈ 23.7 MHz
     
     

4. R = 4.7 kilohms, L = 2 microhenrys, C = 30 picofarads

   • L = 2 × 10^-6 H

   • C = 30 × 10^-12 F

   • f = 1 / (2π√(2 × 10^-6 × 30 × 10^-12))

   • f ≈ 20.5 MHz
     
     

5. R = 4.7 kilohms, L = 15 microhenrys, C = 5 picofarads

   • L = 15 × 10^-6 H

   • C = 5 × 10^-12 F

   • f = 1 / (2π√(15 × 10^-6 × 5 × 10^-12))

   • f ≈ 18.4 MHz
     
     

6. R = 4.7 kilohms, L = 3 microhenrys, C = 40 picofarads

   • L = 3 × 10^-6 H

   • C = 40 × 10^-12 F

   • f = 1 / (2π√(3 × 10^-6 × 40 × 10^-12))

   • f ≈ 14.5 MHz
     
     

7. R = 4.7 kilohms, L = 40 microhenrys, C = 6 picofarads

   • L = 40 × 10^-6 H

   • C = 6 × 10^-12 F

   • f = 1 / (2π√(40 × 10^-6 × 6 × 10^-12))

   • f ≈ 10.3 MHz
     
     

8. R = 4.7 kilohms, L = 10 microhenrys, C = 50 picofarads

   • L = 10 × 10^-6 H

   • C = 50 × 10^-12 F

   • f = 1 / (2π√(10 × 10^-6 × 50 × 10^-12))

   • f ≈ 7.12 MHz
     
     

9. R = 4.7 kilohms, L = 200 microhenrys, C = 10 picofarads

   • L = 200 × 10^-6 H

   • C = 10 × 10^-12 F

   • f = 1 / (2π√(200 × 10^-6 × 10 × 10^-12))

   • f ≈ 3.56 MHz
     
     

10. R = 4.7 kilohms, L = 90 microhenrys, C = 100 picofarads

    • L = 90 × 10^-6 H

    • C = 100 × 10^-12 F

    • f = 1 / (2π√(90 × 10^-6 × 100 × 10^-12))

    • f ≈ 1.68 MHz
      
      

11. Determining Inductance for a Resonant Frequency of 14.25 MHz and C = 44 picofarads

    • f = 14.25 × 10^6 Hz

    • C = 44 × 10^-12 F

    • Rearranging the formula:  L = 1/(4π²f²C) 

    • L ≈ 2.8 microhenrys
      
      

Conclusion

Calculating the resonant frequency in parallel RLC circuits is essential in designing and analyzing circuits for various applications such as radio transmitters, signal processing, and tuning circuits. Understanding how to calculate this frequency using the values of R, L, and C allows engineers to design circuits that resonate at specific frequencies, ensuring optimal performance for their intended use.