Suppose you have a supply of inductors ranging from 1.00 nH to 10.0 H, and capacitors ranging from 1.00 pF to 0.100 F. What is the range of resonant frequencies that can be achieved from combinations of a single inductor and a single capacitor?
Question by OpenStax is licensed under CC BY 4.0
Final Answer

fo max=5.03 GHzf_{\textrm{o max}} = 5.03 \textrm{ GHz}

fo min=0.159 Hzf_{\textrm{o min}} = 0.159 \textrm{ Hz}

Solution video

OpenStax College Physics for AP® Courses, Chapter 23, Problem 97 (Problems & Exercises)

OpenStax College Physics, Chapter 23, Problem 97 (PE) video thumbnail

In order to watch this solution you need to have a subscription.

Start free trial Log in
vote with a rating of votes with an average rating of .

Calculator Screenshots

  • OpenStax College Physics, Chapter 23, Problem 97 (PE) calculator screenshot 1
Video Transcript
This is College Physics Answers with Shaun Dychko. Given a collection of inductors ranging from 1 nanohenrys up to 10 henrys and some capacitors from 1 picofarad up to 0.1 farads, what resonant frequency range can we create? So, the resonant frequency is 1 over 2 Pi times square root times of inductance times capacitance. So, the maximum possible resonant frequency we could have is by minimizing this denominator. And so, we want to minimize inductance and capacitance. So, we have 1 over 2 Pi times square root of 1 nanohenry, which is times 10 to the minus 9 henrys and 1 picofarad, which is 1 times 10 to the minus 12 farads. And, this works out to 5.03 gigahertz. The minimum resonant frequency will come by taking the maximum inductance and capacitance so that's 1 over 2 Pi times square root of 10 henrys times 0.1 farads, which is 0.159 hertz.