Question

Let two cylindrical conductors connected in parallel, to which potential difference V=170V is applied. The two conductors are made of the same material as the first is 6 times the length of the second and 1/5 the radius of the second. The resistance of the second is 469 ohms. Determine the equivalent resistance

Answer 1

Gives

V=170V

$l_1=6l_2$

$r_2=\frac{r_1}{5}$

We know that

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

$R_2=\frac{\rho l_2}{\pi d_2^2}$

$\frac{R_1}{R_2}=\frac{\frac{\rho l_1}{\pi d_1^2}}{\frac{\rho l_2}{\pi d_2^2}}$

Put value

$\frac{R_1}{R_2}=\frac{6}{25}$

$R_2=469\Omega$

$R_1=469\times \frac{6}{25}=112\Omega$

$R_{net}=R_1||R_2$

$R_{net}=\frac{R_1R_2}{R_1+R_2}$

$R_{net}=\frac{112\times469}{112+469}=90\Omega$