Two heater coils made of the same material are connected in parallel across the mains : the length and the diameter of one coil is double that of the other . Which of them will produce more heat?

Explanation

According to Joule heating , the rate at which heat is produced in a resistance is given by `P = I^(2) R = V^(2)// R`. And in parallel , `V` is same , i.e, `V_(1) = V_(2)` . So,
`(P_(2))/(P_(1)) = (R_(1))/(R_(2)) = (L_(1))/(L_(2)) [ (r_(2))/(r_(1))]^(2)` `[ as R = rho(L)/( pir^(2))]`
`= (L_(1))/(2 L_(1))[ (2r_(1))/(r_(1))]^(2)` `[ as L_(2) = 2L_(1) and r_(2) = 2 r_(1)]`
or `P_(2) = 2 P_(1)`
That is heat produced in the thicker coil is more ( i.e, double) than that produced in the other coil.