A dc current of 60 mA can cause paralysis of the body's respiratory muscles and hence interfere with breathing, but only 15 mA (rms) of ac current will do the same thing. Suppose a person is working with electrical power lines on a warm humid day and therefore has a low body resistance of 1400 Ω . What dc V dc and what ac (amplitude V 0 and rms V rms ) potentials would it take to cause respiratory paralysis?

Explanation:

d c current that can cause paralysis

= 60 x 10⁻³ A.

If body resistance = 1400 ohm

d c voltage that can generate the current above

= resistance x current

= 1400 x 60 x 10⁻³

= 84 V .

a c current ( rms ) that can cause paralysis

= 15 x 10⁻³ A.

a c voltage (rms ) that can generate the current above

= resistance x current

= 1400 x 15 x 10⁻³

Vrms = 21  V

maximum amplitude of ac voltage

= √2 x 21

= 29.7 V

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west

where is the