Question

A current of 2A produces 200 J of heat in a wire in a given period of time. If the current is increased to 4 A, how much heat will be produced in the same time?

Answer 1

Answer:

A current of 2A produces 200J of heat in a wire in a given period of time if the current increase is 4A

We have to find heat produced.

By using formula H = I²RT

H1/H2 = I²/I'²

By putting values in the above equation we get,

H2= 200×16/4 = 800J.

Answer: 800J heat will be produced in same time.

Answer 2

Solution :-

Given :-

▪ A current of 2A produces 200J of heat in a wire in a given period of time.

To Find :-

▪ How much heat will be produced in the same time, if current is increased to 4A.

Concept :-

▪ Formula of heat energy produced by electrical instrument in terms of current flow, resistance and time is given by

$\underline{\boxed{\bf{\pink{H=I^2RT}}}}$

• H denotes heat energy
• I denotes current flow
• R denotes resistance
• t denotes time

Calculation :-

Since R and t have constant value, we can say that...

$\implies\bf\:H\propto I^2\\ \\ \implies\sf\:\dfrac{H_1}{H_2}=\dfrac{{I_1}^2}{{I_2}^2}\\ \\ \implies\sf\:\dfrac{200}{H_2}=\dfrac{2^2}{4^2}\\ \\ \implies\sf\:H_2=\dfrac{200\times 16} {4}\\ \\ \implies\boxed{\bf{\purple{H_2=800\:J}}}$