(i). Find the time taken by a filament of `200 W` to heat `500 ml` of water from `25^(@) C to 75 ^(@) C`. Specific heat of water is ` 1 calg^(-1@) C^(-1)`. Take `1 cal = 4.2 J`.
(ii) Find the power produced by each resistor shown in Fig. `7.17`. If `R_(1)` is dipped in `1000 ml` of water at `30^(@) C` , find the time taken by it to boil the water.

Explanation

(i) `200 t = 0.5 xx 4200 xx 50 or t = 525 s`
(ii) `R_(eq) = 6 Omega`,
`I_(1) = 12//6 = 2 A "in" 4 Omega` ,
`I_(2) = 2//3 A "in" 6 Omega `,
`I_(3) = 4//3 A "in" 3 Omega `
`P_(1) = I_(1)^(2) R_(1) = 2^(2) xx 4 = 16 W`
`P_(2) = ((2)/( 3))^(2) xx 6 = (8) /(3) W`
`P_(3) = ((4)/(3))^(2) xx 3 = (16)/( 3) W`
Now ,
`P_(1)t = 1 xx 4200 xx 70 or t = ( 4200 xx 70 )/( 16) = 18,375 s`