Question

The upper portion of the circuit shown in the diagram is fixed while the springs of spring constant $K=10\text{N/m}$ and metal rod are hanging truly. The rod has a length of $5\text{cm}$ and its mass can be neglected for the moment. What should be the value of the resistance $R$ so that the springs elongate by $5\text{mm}$ each, when current passes through the rod.(Give integer value)

Answer 1

Given, $K=10\text{N/m}$ and $B=0.5\text{T}$

The rod is subjected to following forces, when current passes through it

$F_m=BIl$ (downwards)

$F_{spr}=2Kx$ (upwards)

When rod attains equilibrium

$F_m=F_{spr}$

$\Rightarrow BIL=2Kx$

$\Rightarrow 0.5\times I\times 0.05=2\times 10\times 0.005$

$\Rightarrow I=4\text{A}$

Using, $I=\frac{E}{R}$

$\therefore R=\frac{E}{I}=\frac{40}{4}=10\Omega$

Accepted answer : $10$