Question

Electrosurgical units (ESUs) supply high-frequency electricity from resonant RLC circuits to cut, coagulate, or otherwise modify biological tissue. HINT (a) Find the resonance frequency (in Hz) of an ESU with an inductance of L-1.75 ?? and a capacitance of 46.0 nF. Hz (b) Calculate the capacitance required (in F) for a resonance frequency of 2.03 MHz.

Answer 1

The resonance frequency of an ESU can be calculated using the formula 1 / (2π√(LC)). For the given values of inductance and capacitance, the resonance frequency is approximately 1.6 MHz. To find the capacitance required for a specific resonance frequency, rearrange the formula to solve for capacitance and calculate the value.

Step-by-step explanation:

The resonance frequency (in Hz) of an ESU with an inductance of L = 1.75 H and a capacitance of C = 46.0 nF can be calculated using the formula:

Resonance frequency = 1 / (2π√(LC))

Plugging in the values, we get:

Resonance frequency = 1 / (2π√(1.75 H * 46.0 nF))

Simplifying further, the resonance frequency is approximately 1.6 MHz.

For the second part of the question, to find the capacitance required (in F) for a resonance frequency of 2.03 MHz, we can rearrange the formula as follows:

Capacitance = 1 / (4π²f²L)

Substituting the known values, we have:
Capacitance = 1 / (4π² * (2.03 MHz)² * 1.75 H)
Calculating, the required capacitance is approximately 26.5 pF.