Electronic – How to calculate the safe AC frequency at high Voltages

Find the input admittance

$$Y = j\omega C + \frac{1}{R+j\omega L} = j\omega C + \frac{R-j\omega L}{R^2+\omega^2 L^2}$$ $$Y = \frac{R}{R^2+\omega^2 L^2} + j(\omega C + \frac{-\omega L}{R^2+\omega^2 L^2}) $$

Then the Resonant Fequency is when the Imaginary component of the input admittance is zero$$Im(Y)=0$$

So $$\omega C + \frac{-\omega L}{R^2+\omega^2 L^2} = 0$$

$$\omega C = \frac{\omega L}{R^2+\omega^2 L^2} $$

$$\frac{C(R^2+\omega^2 L^2)}{L} =1 $$

$$\frac{R^2C+\omega^2 CL^2}{L} =1 $$

$$\frac{R^2C}{L}+\omega^2 LC =1 $$

$$\omega^2 LC = 1 - \frac{R^2C}{L} $$

I bet you can take it form here

The typical current to kill a healthy person is many mA.

The minimum amount that could be harmful for a person not in perfect health might be a lot less, or if the current could be directly under the skin directly to the heart it will most certainly be less. The latter is the primary reason why medical power supplies must have leakage in the \$\mu\$A range. See, for example, this, which has references to some relevant standards (which have to be purchased).

In the more general (non-medical) marketplace, you can refer (for US purposes) to UL 508A 43.1.2 which (IIRC) specifies 42.4VDC/30VAC RMS.

Something that is a bit less than the typical amount to kill a healthy person cannot be considered "safe" under all conditions. Fewer precautions are necessary for voltages less than about 20-50V given normal skin resistance, which is why 9V batteries, 12V automotive electrical systems, and 18VAC doorbell transformers don't generally kill people. It's more than enough voltage to cause enough current to kill you if applied below the skin surface, through your heart.

High voltage at limited current or limited energy is not generally a problem- a static charge in the thousands of volts typically only causes a bit of discomfort.

For most purposes, 24VDC or lower will be considered safe enough. Most (non-electric/hybrid) electrical systems are in this range, 24VDC is very common industrial controls, many laptops use a voltage a bit under 20VDC for the chargers etc.

For a real answer though, you should seek out all the regulations that apply to your situation and your jurisdiction and ensure compliance with each of the requirements.