Question

What capacitance in pF will resonate with a 305pH inductor to produce a signal with a wavelength of 36mm?

Answer 1

To find the capacitance needed to resonate with an inductor and produce a signal with a specific wavelength, convert the wavelength to meters, use the formula wavelength = 2π√(LC), rearrange the formula to solve for capacitance, substitute the given values, and convert the capacitance to picofarads.

Step-by-step explanation:

To calculate the capacitance needed to resonate with an inductor and produce a signal with a specific wavelength:

1. Convert the wavelength from mm to meters.
2. Use the formula: wavelength = 2π√(LC), where L is the inductance and C is the capacitance.
3. Rearrange the formula to solve for capacitance: C = (wavelength^2) / (4π^2L).
4. Substitute the given values into the formula to calculate the capacitance in farads.
5. Convert the capacitance from farads to picofarads by multiplying by 10^12.

In this case, the calculated capacitance in pF will resonate with the 305pH inductor to produce a signal with a wavelength of 36mm.

Note: Ensure that all units used in the calculation are consistent (e.g. meters for wavelength and Henrys for inductance).