Resonant Frequency in Parallel CIRCUITS
Section A-001-004
Section A-001-004
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.
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
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
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
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
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
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
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
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
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
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
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
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
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.