Question

Two wires made of the same material are connected in parallel

across the mains. The length and radius of one wire is two
times that of the other wire. If heat produced in the shorter wire
is 100 J, then the heat produced in the longer wire is:-
O A. 100 J
B. 180 J
O C. 2003
O D. 420 J​

Answer 1

The heat produced in the longer wire is 200 J.

Step-by-step explanation:

When the two wires are connected in parallel then the voltage across both the wires is same.

Let the length of the second wire is L and the radius of the second wire is R.

The length of the first ire is 2L and the radius of the first wire is 2R.

Heat produced in the second wire is 100 J.

Let the heat produced in the first wire is H'.

The resistance of the wire is proportional to length of the wire and inversely proportional to the area of the wire.

`(R_2)/(R_1)=(L* \pi* 4R^2)/(2L* \pi* R^2)\\\\(R_2)/(R_1)=2`

The heat produced is given by

`H=(V^2)/(R)\\\\(H_1)/(H_2)=(R_2)/(R_1)\\\\(H_1)/(100)=2\\\\H_1=200 J`