What is the resonant frequency of a tuned circuit consisting of a 500 picofarad capacitor, a 150 microfarad tuning coil, and 10 ohms resistance?

What is the resonant frequency of a tuned circuit consisting of a 500 picofarad capacitor, a 150 microfarad tuning coil, and 10 ohms resistance?

• A. 581 kHz
• B. 753 kHz
• C. 498 kHz
• D. None of the above

Answer: (A)

The resonant frequency of a tuned circuit, specifically an LC circuit (which includes an inductor and a capacitor), can be calculated using the formula: \[ f = \frac{1}{2\pi\sqrt{LC}} \] where \( f \) is the resonant frequency in hertz (Hz), \( L \) is the inductance in henries (H), and \( C \) is the capacitance in farads (F). In this scenario, the capacitor’s value is given as 500 picofarads (pF), which can be converted to farads: \[ 500 \, \text{pF} = 500 \times 10^{-12} \, \text{F} = 5 \times 10^{-10} \, \text{F} \] The tuning coil (inductor) is given as 150 microhenries (µH), which can be converted to henries: \[ 150 \, \text{µH} = 150 \times 10^{-6} \, \text{H} = 1.5 \times 10^{-4} \, \text{H} \] Substituting these values into

The resonant frequency of a tuned circuit, specifically an LC circuit (which includes an inductor and a capacitor), can be calculated using the formula:

[ f = \frac{1}{2\pi\sqrt{LC}} ]

where ( f ) is the resonant frequency in hertz (Hz), ( L ) is the inductance in henries (H), and ( C ) is the capacitance in farads (F).

In this scenario, the capacitor’s value is given as 500 picofarads (pF), which can be converted to farads:

[ 500 , \text{pF} = 500 \times 10^{-12} , \text{F} = 5 \times 10^{-10} , \text{F} ]

The tuning coil (inductor) is given as 150 microhenries (µH), which can be converted to henries:

[ 150 , \text{µH} = 150 \times 10^{-6} , \text{H} = 1.5 \times 10^{-4} , \text{H} ]

Substituting these values into