A copper wire, $2\,\text{m}$ long, has a circular cross-section. It carries a steady current when it is attached to a mobile phone so that the battery can be charged. The wire is defective. Over a $1\,\text{m}$ section, the diameter is half that of the remaining $1\,\text{m}$ section. The power dissipated in the wider section of wire is $P$. What power is dissipated in the narrower section of wire?
- A$\frac{1}{4}P$
- B$\frac{1}{2}P$
- C$2P$
- D$4P$