If it takes 8 minutes to boil a quantity of water
electrically, how long will it take to boil the same
quantity of water using the same heating coil
but with the current doubled
Answers
Time = 8 minutes *(1/2)^2 = 2 minutes. Explanation is given below:
You know that:
heat = voltage * current* time,
heat = (current*resistance)* current* time,
= (current)^2 * resistance * time
let us say that heat is "Q", when current "I" is passed for 8 minutes through heater of R ohms.
Q = I^2 * R * 8 ------------- (1)
If current is doubled (to 2I) for some time to get same heat, the equation becomes:
Q =(2I)^2 * R * time.
= 4I^2 *R * time ------------(2)
Approach1: Divide both sides of equation (2) by corresponding sides of equation (1):
Q/Q = 4I^2*R*time / I^2 * R * 8
1 = 4time/8
time = 8/4 = 2
Approach2: as lefthand side of equation (1) is equal to left hand side of equation (2), right hand sides of the both the equations must be equal.
Therefore:
4I^2 *R * time = I^2 * R * 8
4 time = 8
time = 2 minute