A 6 m long wire made from an alloy,nichrome,is shaped into coil and given for producing heat.It has a resistance of 24 ohm.Can we get more heat if the wire is cut into half of its original length and shaped into a coil? For getting energy,the two ends of the wire are connected to a source with a potential difference of 220 V.

Answer

More heat will be obtained after cutting the wire into half.

Explanation

Let R be the resistance of the whose wire and V be the potential difference between the two ends.
Given that, `R=240Omega, V=220V.`
For coil of whole wire,
Power `(P_(1))=(V^(2))/(R)=(220^(2))/(240)=(220xx220)/(240)`
`=220xx(11)/(12)=(2420)/(12)=201.67W`
For coil of half length wire,
`"Power "(P_(2))=(V^(2))/((R//2))`
`" ..."(because "As length is reduced to half, the resistance will also become half")`
`therefore" "P_(2)=((220)^(2))/((240//2))=(220^(2))/(120)=(220xx220)/(120)=220xx(11)/(6)`
`=(2420)/(6)`
Comparing `P_(1) and P_(2)`, we can say `P_(2) gt P_(1)`.