Grounding Rods

[P_A]

True or false:

1. The ground resistance is inversely proportional to the diameter of the ground rod. T or F?
   
2. The ground resistance is inversely proportional to the length of the ground rod. T or F?
   

According to Zach's AIT question #7: these statement are false, but they look true to me. Because:

1. Doubling the length/depth of a ground electrode reduces resistance by 40%.

2. Doubling the diameter of a ground electrode only decreases resistance by 10%.

 

[akyip]

I think when Zach says proportional, he means it can be either directly multiplied or divided between one number and another number. Basically, proportional means:

a = n * b

I guess there is a difference between directly or inversely related, and directly or inversely proportional.

@Zach Stone, P.E.: can you put any input on this?

 

[DarkLegion PE]

I agree with you, if you increase the length or diameter the resistance decreases. I was also tripped up by this, I think it's definitely a wording thing here at play 

 

[Sparky Bill PE]

Following for response.

 

[Zach Stone P.E.]

True or false:

1. The ground resistance is inversely proportional to the diameter of the ground rod. T or F?
   
2. The ground resistance is inversely proportional to the length of the ground rod. T or F?
   

According to Zach's AIT question #7: these statement are false, but they look true to me. Because:

1. Doubling the length/depth of a ground electrode reduces resistance by 40%.

2. Doubling the diameter of a ground electrode only decreases resistance by 10%.

Both inversely proportional, and directly proportional are a linear, 1 to 1 relationship.

If two values are inversely proportional, as one value increases the other decreases by the same amount and vice versa.

If two values are directly proportional, as one value increases, the other also increases by the same amount and vice versa.

For example, Ohm's Law V = IZ. Voltage and current are directly proportional, but current is inversely proportional to impedance (I=V/Z).

A natural log (ln), like the one in the formula for this problem, is not a linear relationship:

I think when Zach says proportional, he means it can be either directly multiplied or divided between one number and another number. Basically, proportional means:

a = n * b

I guess there is a difference between directly or inversely related, and directly or inversely proportional.

@Zach Stone, P.E.: can you put any input on this?

you got it.

 

[DarkLegion PE]

Both inversely proportional, and directly proportional are a linear, 1 to 1 relationship.

If two values are inversely proportional, as one value increases the other decreases by the same amount and vice versa.

If two values are directly proportional, as one value increases, the other also increases by the same amount and vice versa.

For example, Ohm's Law V = IZ. Voltage and current are directly proportional, but current is inversely proportional to impedance (I=V/Z).

A natural log (ln), like the one in the formula for this problem, is not a linear relationship:



you got it.

Thanks this is a great explanation. NCEES practice 77 trapped me with this if anyone wants to practice with it

 

[akyip]

Thanks this is a great explanation. NCEES practice 77 trapped me with this if anyone wants to practice with it

I'm pretty sure I know which question you're talking about:

The one about charging line current, you're asked if it's directly proportional to voltage, line length, capacitance, and radius (I think).

I chg = Vs LN / Xc = Vs LN / (1/wC) = w * C * Vs LN

So the charging current is directly proportional to the voltage, capacitance, and line length ( C = C per unit length * line length). It is also related to conductor radius, but not direct proportion since the capacitance formula is related to the ln of (GMD/r).

 

[DarkLegion PE]

I'm pretty sure I know which question you're talking about:

The one about charging line current, you're asked if it's directly proportional to voltage, line length, capacitance, and radius (I think).

I chg = Vs LN / Xc = Vs LN / (1/wC) = w * C * Vs LN

So the charging current is directly proportional to the voltage, capacitance, and line length ( C = C per unit length * line length). It is also related to conductor radius, but not direct proportion since the capacitance formula is related to the ln of (GMD/r).

exactly the one yup!