The water in an electric kettle begins to boil in 15 minutes after being switched on. If the water is to boil in 10 minutes using the main supply, the length of heating element be
(1) Increased to 3/2 value
(2) Decreased to 2/3 of its value
(3) Increased to 5/4 of its value
(4) Decreased to 4/5 of its initial value.
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Answer:
decreased to 2/3 of it's value
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Answer:
(2) Decreased to 2/3 of its value
Explanation: The power of the kettle = V²/ R
Initial heat, H = V²/ R × 15 J
Let the new resistance be Rₙ
Now, final heat, Hₙ = V²/ Rₙ × 10 J
Since energy is same,
⇒ H = Hₙ
⇒ V²/ R × 15 J = V²/ Rₙ × 10 J
⇒ 3/R = 2/Rₙ
∴ Rₙ/R = Lₙ/ L = 2/3
Hence, the length of the heating element should be decreased to 2/3 of its value.
Additional information:-
(1) Resistance of a conductor = ρl/A where R ∝ l and R ∝ 1/A
(2) If resistance R is changed to Rₙ then length also changes from L to Lₙ
i.e. Rₙ/R = Lₙ/ L as R ∝ l
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