An electric kettle has two coils. When one coil is switched on, it takes 10 min to boil water and when the second coil is switched on it takes 20 min to boil same amount of water. The time taken by electric kettle to boil water when-both coil are used in parallel, is found to be n second. Find the value of n .

Step-by-step solution

Heat produced in a resistance R in time t is given by H= V^2 R t[ where , V= source voltage ] For first coil, H₁= V^2 R₁ t₁= V^2 R₁ 10 60 [ t₁=10 60 ~s ] For second coil, H₂= V^2 R₂ t₂ [ t₂=20 60 ~s ]= V^2 R₂ 20 60 Given that, H₁=H₂ array ll & V^2 R₁ 10 60= V^2 R₂ 20 60 & R₂=2 R₁..(i) array Let t be the time taken by electric kettle to boil water when both coil are used in parallel, then aligned H_p= & ( V^2 R₁ + V^2 R₂ ) t=V^2 t ( 1 R₁ + 1 2 R₁ )[ from Eq. (i) ] & H_p= 3 V²t 2 R₁ aligned But, H_P=H₁ 3 V^2 t 2 R₁ =