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Water boils in an electric kettle in 15 ...

Water boils in an electric kettle in 15 mins, after switching on. If the length of the heating wire is decreased to `(1)/(3)` of its initial value ,then in how much time will the same amount of water boil with the same supplyvoltage ?

Text Solution

Verified by Experts

Supply Voltage is same
Amount of heat produced is also same
Time taken to heat water t = 15min
`H = (V^(2))/("R") .t [H = I^(2)Rt implies (V = IR) therefore I = (V)/("R") ]`
`therefore (R_(1))/(R_(2)) = (t_(1))/(t_(2))`
`R prop l [R = rho(l)/(A)]`
`(R_(1))/(R_(2)) = (l_(1))/(l_(2))`
From (1) and (2)
`(l_(1))/(l_(2)) = (t_(1))/(t_(2)) = (15)/(t_(2))`
`l_(2) = (1)/(3)l_(1) implies (l_(1))/(l_(2)) = 3`
sub in (3) 3 =`(15)/(t_(2))`
`therefore t_(2) = (15)/(3) = 5 `min
Time taken to heat `(1)/(3)` length of the wire = 5 min
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