Final answer:
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:
- Convert the wavelength from mm to meters.
- Use the formula: wavelength = 2π√(LC), where L is the inductance and C is the capacitance.
- Rearrange the formula to solve for capacitance: C = (wavelength^2) / (4π^2L).
- Substitute the given values into the formula to calculate the capacitance in farads.
- 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).