Question

What is the resonant frequency of a series RLC circuit when L=250H,C=400pF and R=10Ω

Answer 1

The resonant frequenccy of the RLC circuit is approximately 159.2 Hz.

Step-by-step explanation:

In an RLC series circuit, the resonant frequency can be calculated using the formula:

fr = 1 / (2π √(LC))

Plugging in the given values of L=250H and C=400pF into the formula, we get:

fr = 1 / (2π √(250H × 400pF))

Simplifying this expression, we can convert the units to farads and henries:

fr = 1 / (2π √(250 × 10-6 F × 400 × 10-12 H))

fr = 1 / (2π √(0.1 x 10-6))

fr = 1 / (2π × 10-3)

fr = 1 / (0.00628)

fr ≈ 159.2 Hz

So, the resonant frequency of the series RLC circuit is approximately 159.2 Hz.

Answer 2

The resonant frequency of the given series RLC circuit with L=250H, C=400pF, and R=10Ω is approximately 503.29 kHz.

Step-by-step explanation:

The resonant frequency of a series RLC circuit is determined using the formula f_r = 1 / (2π√(LC)), where f_r is the resonant frequency, L is the inductance in henries (H), and C is the capacitance in farads (F). Given the values L = 250 H and C = 400 pF, we first convert picofarads to farads: C = 400 pF = 400 x 10^-12 F. Now, we can calculate the resonant frequency:

f_r = 1 / (2π√(250 H * 400 x 10^-12 F)) = 1 / (2π√(100 x 10^-9 H*F)) = 1 / (2π√(100 x 10^-9)) = 1 / (2π * 10^-4.5) ≈ 1 / (6.2832 * 3.1623 x 10^-5) ≈ 503.29 kHz.

Hence, the resonant frequency of the series RLC circuit is approximately 503.29 kHz.