Question

A wire of length L is used in an electric heater. When the potential

difference across the wire is 200 V, the power dissipated in the wire is
1000 W. The same potential difference is applied across a second similar wire of
length 2L. What is the power dissipated in the second wire?

Answer 1

Answer:500 W

Step-by-step explanation:

Given

When length is L power dissipated is
`100\ W`

Potential difference applied is
`200\ V`

Resistance of wire is directly proportional to length of wire

Suppose initially Resistance is R

When L changes to
`2L`

Resistance changes to
`2R`

Initial Power dissipated is
`P_o=(V^2)/(R)`

For 2 R resistance and same voltage, Power dissipated is

`P_1=(V^2)/((2R))`

So
`P_1=(1)/(2)* (V^2)/(R)`

`P_1=(P_o)/(2)`

So
`P_1=(1000)/(2)`

`P_1=500\ W`