Maths problem

Question

the resistace R of a wire is directly proportional to its length. If R=40mohms for a wire 10 cm long , find the resistance R in mohms :

a) when the length decreases to 6cm

b) when the length decreases by 25%

Answer 1

Hi Danish,

 

We can rewrite "the resistace R of a wire is directly proportional to its length" as R=αL where R is the resistance, α the proportionality factor, and L the length of the wire.

 

Since " R=40mohms for a wire 10 cm long", we can write the direct proportionality in Math form as (40mΩ/10cm).  This means that we don't have to worry about α.

 

a) when the length decreases to 6cm, we can setup the following equation

(40mΩ/10cm)=(xmΩ/6cm)

Now, solving for x through cross multiplication, we get x=24mΩ

 

b) when the length decreases by 25%

Since the original length was 10cm, a 25% decrease means that the length was shortened by 2.5cm.  So, the final length is now 7.5cm.  Setting up a proportionality form as before, we get:

(40mΩ/10cm)=(ymΩ/7.5cm)

Solving for y through cross multiplication, we get y=30mΩ

 

Hope this helps!