Ram ans Shyam purchased two electric tea kettles A and B of same size, same thickness, and same volume of 0.4L. They studied the specification of kettles as under
`Kettle A: `
specific heat capacity `= 1680 Jkg^(-1)K^(-1)`
Mass = 200 g
Cost = Rs. 400
Kettle B:
Specific heat capacity = `2450 Jkg^(-1) K^(-1)`
Mass = 400 g
Cost = Rs. 400
When kettle A is switched on with constant potential source, the tea begins to boil in 6 min. When kettle B is switched on with the same source separately, then tea begins to boil in 8 min. The efficiengy of kettle is defined as
(Energy used for liquid heating)/(Total energy supplied)
They made discussion on specification and efficiency of kettles and subsequently prepared a list of questions to draw the conclusions. Some of them are as under (assume specific heat of tea liquid as `4200J kg^(-1)K^(-1)` and density `1000 kgm^(-3)`
If both the kettles are joined with the same source in series one after the other, then boiling starts in kettle A and kettle B after

Options

A. four times of their original time
B. equal to their original time
C. two times of their original time
D. cannot be ascertained by above data.

Answer

A

Explanation

a. (i) `V^2/R_(A) xx 6 = V^2/(R_A + R_(B))^2 R_(A) xx t_(A)`
But `R_(A) = R_(B) or V^2/R_(A) xx 6 = V^2/R_(A) xx 6 = V^2/(4R_(A)^(2)) R_(A) xx t_(A)`
`t_(A) = 24min.`
(ii) `V^2/R_(B) xx 8 = V^2/(R_(A)+R_(B))^2 R_(B) xx t_(B)`
`8/R_(B) = R_(B)/(4R_(B^2)) t_(B) or t_(B) = 32min.`