Question

A wire is used as a heating element that has a resistance that is fairly independent of its temperature within its operating range. When a current I flows through the wire, the energy delivered by the heater each minute is E. For what amount of current will the energy delivered by the heater each minute be 4E?

Answer 1

Double the current

Step-by-step explanation:

The energy delivered by the heater is related to the current by the following relation:

E=
`I^(2)R t`

let R * t = k ( ∴ R and t both are constant)

so E= k
`I^(2)`

Now let:

E2= k I₂^2

E2= 4E

⇒ k I₂^2= 4* k
`I^(2)`

Cancel same terms on both sides.

I₂^2= 4*
`I^(2)`

taking square-root on both sides.

√I₂^2 = √4* I^2

⇒I₂= 2I

If we double the current the energy delivered each minute be 4E.