Question

A radio tuning circuit contains an RLC circuit with a resistorof R=4 Ohms, and an inductor of L=3.0 µH.

(a) What capacitance is needed to produce aresonant frequency of 95 MHz?
___________pF

Answer 1

To achieve a resonant frequency of 95 MHz with an inductance of 3.0 µH, a capacitance of approximately 17.8 picofarads (pF) is required in the RLC circuit.

Step-by-step explanation:

To calculate the capacitance needed to produce a resonant frequency of 95 MHz in an RLC circuit with a given inductance of 3.0 µH, we use the formula for the resonant frequency of an RLC circuit:

f = \( \frac{1}{2\pi\sqrt{LC}} \)

Where:

• f is the frequency in hertz (Hz)
• L is the inductance in henry (H)
• C is the capacitance in farads (F)

We can rearrange this formula to solve for C:

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

Plugging in the values:

C = \( \frac{1}{(2\pi \cdot 95 \times 10^6)^2 \cdot 3.0 \times 10^{-6}} \)

After calculating, we find that the capacitance C is:

C ≈ 17.8 pF

Therefore, a capacitance of approximately 17.8 picofarads (pF) is needed to achieve a 95 MHz resonant frequency in the given RLC circuit.