Fuse Wire Length and Capacity: A Discussion

[Vagrant]

Homework Statement

does the length of the fuse wire influence its cpacity? why?

Homework Equations

R=pL/a

The Attempt at a Solution

My teacher said no. I think it should because R depends on L


Thanks for your time.

 

[Andrew Mason]

Homework Statement

does the length of the fuse wire influence its cpacity? why?

Homework Equations

R=pL/a

The Attempt at a Solution

My teacher said no. I think it should because R depends on LThanks for your time.

I think I would agree with your teacher. The fuse capacity (the largest current permitted to flow) depends on the temperature of the fuse wire. At a certain temperature, it melts and stops the current. Off hand, I would say that the temperature depends upon the power density being dissipated in the fuse wire (power / unit volume). The power dissipated is $I^2R = I^2\rho L/A$

Now, the power per unit volume is:

$$P/Vol = P/LA = I^2\rho L/A(LA) = I^2\rho/A^2$$

So it appears to me that the L falls out and the temperature depends entirely upon the cross sectional area of the fuse wire.

AM

 

[Vagrant]

Thanks. I think your answer makes sense.