What is the RMS Voltage Across a Body Near a Transformer?

[andrew410]

A person is working near the secondary of a transformer, as shown in the figure below. The primary voltage is 120 V at 60.0 Hz. The capacitance C, which is the stray capacitance between the hand and the secondary winding, is 10.0 pF. Assuming that the person has a body resistance to ground R, determine the rms voltage across the body. (Suggestion: Redraw the circuit with the secondary of the transformer as a simple AC source.)
FIGURE: http://east.ilrn.com/graphing/bca/user/appletImage?dbid=445132339

I need some help with this stuff. This is what I know already. I know that the secondary voltage is 6000 V according to the figure. Also, I know that the rms voltage = max voltage/sqrt(2). I'm not sure how to get the max voltage. I tried using the secondary voltage as the max voltage, but the answer wasn't right. So, I think the secondary voltage is the AC source. How do I get the max voltage using the secondary voltage? Maybe I'm doing this all wrong? I don't know...any help would be great! Thx in advance! :)

 

[Gamma]

How about trying this? Let the voltage (secondary) as

$$v=v_0 e^{jwt}$$

Find the current through the circuit i, using ohms law.

$$v_0 e^{jwt} = i (R_b -\frac{j}{wc})$$

where -j/wc is the impedance of the capacitor.

Find the charge of the capacitor q by integrating current i since
i = dq/dt

use q= Cv to find the voltage across the capacitor $$v_c$$

therefore, voltage across the body $$v_b = v - v_c$$

absolute value of the vb is the max voltage created across the person's body. I am getting this to be about 23 volts using the human body resistance of 1 Mega ohm, causing a current of about 0.023 mA to flow through him. Hopefully it would not kill him.

 

[thepatientmental]

Hi there,

First of all, let's redraw the circuit as suggested. We can simplify the secondary of the transformer as a simple AC source with a voltage of 6000 V. The stray capacitance C can be represented as a capacitor in parallel with the body resistance R, which is connected to ground.

Now, we can use the formula V = IZ to find the voltage across the body, where Z is the impedance of the circuit and I is the current flowing through it. We can find the impedance by using the formula Z = 1/(jωC + 1/R), where j is the imaginary unit and ω is the angular frequency (2πf).

So, plugging in the values we have, we get Z = 1/(j2π(60)(10x10^-12) + 1/R) = 1/(j0.012 + 1/R). Now, we need to find the current I. We can use Ohm's law, V = IR, to find the current. Since we know the voltage (6000 V) and the resistance (R), we can solve for I.

Finally, we can use the formula V = IZ to find the voltage across the body, which will give us the maximum voltage. We can then use the formula Vrms = Vmax/sqrt(2) to find the rms voltage across the body.

I hope this helps you understand how to approach this problem. Let me know if you have any further questions. Good luck!