Question

If the potential difference is applied across a resistor of length l and diameter d .if the diameter will halfed then the V will be

Answer 1

Gives

Patentialdifferrnce=V

resistor=R

Length=l

Diameter (d₁)=d

We know that

$R_1=\frac{\rho l}{A_1}=\frac{\rho l_1}{\pi d_1^2}$

$V=IR_1$

$V_1=I_1\frac{\rho l_1}{\pi d_1^2}$

When

$d_2=\frac{d}{2} ,l_2=2l$

$R_2=\frac{\rho l_2 }{A_2}$

$R_2=8\frac{\rho l_1}{\pi d_1^2}$

$V_2=IR_2$ $;V_2=8I \frac{\rho l}{\pi d_1^2}$

$V_2=8V_1$