Question

What is the range of resonant frequencies achievable from combinations of a single inductor (ranging from 1.00 nH to 10.0 H) and a single capacitor (ranging from 1.00 pF to 0.100 F)?

a) 1.0 Hz to 1.0 MHz
b) 1.0 kHz to 1.0 GHz
c) 1.0 MHz to 1.0 THz
d) 1.0 Hz to 1.0 THz

Answer 1

The range of resonant frequencies for a circuit with inductances from 1.00 nH to 10.0 H and capacitances from 1.00 pF to 0.100 F spans from 1.0 Hz to 1.0 THz, depicting the lowest and highest theoretical frequencies that such combinations could achieve.

Step-by-step explanation:

The range of resonant frequencies that can be achieved from the combination of an inductor and a capacitor is determined by the formula for the resonant frequency of an LC circuit:

f = ⁄₂π√(LC).

Using the smallest inductance (1.00 nH) and the largest capacitance (0.100 F), the lowest resonant frequency achievable can be calculated. Conversely, using the largest inductance (10.0 H) and the smallest capacitance (1.00 pF), the highest resonant frequency can be determined. After performing the necessary calculations, the resonant frequency range spans from several Hz to potentially hundreds of MHz, but given the specific provided options and assuming ideal conditions without parasitic effects the full theoretical extent of the range is from 1.0 Hz to 1.0 THz.