An electric tea kettle has two heating coils. When one of the coils is switched on, boiling begins in 6 min. When the other coil is switched on, the boiling begins in 8 min. In what time, will the boiling begin if both coils are switched on simultaneously (i) in series and (ii) in parallel.

Explanation

Let power of first coil is `P_(1)` and that of second coil is `P_(2)`. Let H is the amount of heat required to oil water.
Then `H=P_(1)t_(1)=p_(2)t_(2)` where `t_(1)="6 min, "t_(2)="8 min"`
i) When the coils are connected in series :
`P=(P_(1)P_(2))/(P_(1)+P_(2))" "t=(H)/(P)=H[(1)/(P_(1))+(1)/(P_(2))]=H[(t)/(H)+(t_(2))/(H)]`
`=t_(1)+t_(2)=6+8="14 min"`
ii) When the coils are connected in parallel `P=P_(1)+P_(2)`
`t=(H)/(P)=(H)/(P_(1)+P_(2))=(H)/((H)/(t_(1))+(H)/(t_(2)))=(t_(1)t_(2))/(t_(1)+t_(2))=(6xx8)/(6+8)="3.43 min."`