Question

A person is working on a steel structure while standing on the ground. An accident occurred where 5 A pass through the structure to the ground. The structure is grounded by a metal rod 6cm in diameter. The rod is dug 2m into the ground. The surrounding soil is dry. Assume that the resistance of the man’s body is 2000 Ω. Compute the current through the man.

Answer 1

Answer:

35mA

Explanation:

Hello!

To solve this problem we must use the following steps

1. Find the electrical resistance of the metal rod using the following equation

$R=\alpha \frac{l}{a}$

WHERE

α=

metal rod resistivity=2x10^-4 Ωm

l=leght=2m

A=  Cross-sectional area

$A=\frac{\pi }{4} d^2=\frac{\pi }{4} (0.06)^2=0.00283$

solving

$R=(2x10^-4)\frac{2}{0.00283} =0.14$

2. Now we model the system as a circuit with parallel resistors, where we will call 1 the metal rod and 2 the man(see attached image)

3.we know that the sum of the currents in 1 and 2 must be equal to 5A, by the law of conservation of energy

I1+I2=5

4.as the voltage on both nodes is the same we can use ohm's law in resitance 1 and 2 (V=IR)

V1=V2

(0.14I1)=2000(i2)

solving for i1

I1=14285.7i2

5.Now we use the equation found in step 3

14285.7i2+i2=5

$i2=\frac{5}{14285.7+1} =3.5x10^-4A=35mA$