# Homework Help: Current homework problem

1. Dec 3, 2009

### captainjack2000

1. The problem statement, all variables and given/known data
A light bulb has a straight metal wire filament of 50 micro metres diameter and 10mm long and when powered with a 5V constant voltage supply it draws 0.5A of current. What happens to the current if the filament is replaced with one of three times the diameter?

2. Relevant equations
I=nAvQ ??

3. The attempt at a solution

2. Dec 3, 2009

### mikelepore

Re: Current

Look at the formula for the resistance of a resistor in terms of its physical dimensions.

3. Dec 3, 2009

### captainjack2000

Re: Current

Thanks

So
R=l * rho /A
where l is the length of the conductor
rho is the electrical resistivity of the material
A is the cross-sectional area of the conductor

So V=IR
I(1) = V/R(1) and I(2)=V/R(2) where I(1) is the inital current
taking a ratio
I(1)/I(2) = [V/R(1)]/[V/R(2)] = R(2)/R(1) = [l(2)*rho*A(1)] /[l(1) * rho* A(2)]
rho is the same for each and l is the same for each so
I(1)/I(2) = A(1)/A(2)
= (pi * r(1) ^2) / (pi* r(2) ^2)
=r(1)^2 / r(2) ^2 where r(1) and r(2) are the corresponding radii of the filaments
=(25*10^-6)^2 / (75*10^-6)^2

so I2=4.5A

Is that right?

4. Dec 5, 2009

Re: Current