Babita K. answered • 03/08/17

Math, Science, and Writing Tutor with Lots of Experience

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)=(

**x**mΩ/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)=(

**y**mΩ/7.5cm)Solving for y through cross multiplication, we get

**y=30mΩ**Hope this helps!