Exam

BITSAT

Year

2023

Paper

Paper 1

Subject

Physics

Chapter

Current Electricity

BITSAT 2023 · Paper 1 · Physics · Current Electricity

The resistance of a wire is 5 . It's new resistance in ohm if...

The resistance of a wire is $5 \Omega$. It's new resistance in ohm if stretched to 5 times of its original length will be :

Step-by-step solution

Let resistance of a wire $R$ and length 1.
$\mathrm{R}=\frac{\rho \ell}{\mathrm{A}}=5 \Omega$
$\therefore \quad$ Volume of wire is constant in stretching
$V_i=V_f \Rightarrow A_i \ell_i=A_f \ell_f$
$\mathrm{A} \ell=\mathrm{A}^{\prime}(5 \ell) \Rightarrow \mathrm{A}^{\prime}=\frac{\mathrm{A}}{5}$
$R_f=\frac{\rho \ell_f}{A_f}=\frac{\rho(5 \ell)}{\left(\frac{A}{5}\right)}=25\left(\frac{\rho \ell}{A}\right)=25 \times 5=125 \Omega$