Water boils in an electric kettle in $$15$$ minutes after switching on. If the length of the heating wire is decreased to $$2/3$$ of its initial value, then the same amount of water will boil with the same supply voltage in

Question

Infinity Learn · Accepted Answer

$$H=V2RtSince$$ supply voltage is same and equal amount of heat will be produced, $$thereforeR1t1$$ $$=$$ $$R2t2$$  or  $$R1R2+t1t2But$$  R ∝ l  ⇒ $$R1R2=l1l2By$$ (i) and (ii),$$l1l2$$ $$=$$ $$t1t2$$              …$$(iii)Now$$  $$l2$$ $$=$$ $$23$$ $$l1$$  ⇒  $$l1l2$$ $$=$$  $$32$$∴   By  equation iii,  $$32$$  $$=$$  $$15t2$$  ⇒  $$t2$$ $$=10$$  minutes

Water boils in an electric kettle in 15 minutes after switching on. If the length of the heating wire is decreased to 2/3 of its initial value, then the same amount of water will boil with the same supply voltage in

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