Assuming the person has a body resistance to ground of Rb = 40.0 k , determine the rms voltage across the body.

+2 votes

A person is working near the secondary of a transformer, as shown in the figure. The primary voltage is 120 V at 60.0 Hz. The capacitance Cs, which is the stray capacitance between the hand and the secondary winding, is 23.0 pF. Assuming the person has a body resistance to ground of Rb = 40.0 k image, determine the rms voltage across the body. Suggestion: Redraw the circuit with the secondary of the transformer as a simple AC source. 
 V

image
asked Mar 19, 2012 in Physics by apush ~Expert~ (552 points)
    

1 Answer

0 votes

V rms body  = I rms * R body    (*where V rms body = rms voltage across body, Irms = rms current through circuit, R body = resistance of body)

It is necessary to first find I rms

I rms = V rms / Z   (*where V rms = rms voltage which is 120 V, Z = impedance)

So now we need to find Z:

Z = squareroot ( R body^2 +(XL - XC)^2 )   (*where XL = inductive reactance, XC = capacitive reactance)

Since there is no inductance, XL goes to 0 and we just need to find XC:

XC = 1 / ω*C    (*where  ω = angular frequency , C = capacitance)

ω = 2pi*f     (*where f = frequency)

After finding XC plug back into equation for Z:

After finding Z, I rms can be found.

Then plug I rms back into first equation for solve for V rms body

 

answered Mar 25, 2012 by Roar3215 ~Expert~ (1,318 points)
edited Mar 25, 2012 by Roar3215



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