Answer to Question #249456 in Electric Circuits for Hellow

Question

two cylindrical conductors connected in parallel, to which a potential difference of V = 170V is applied. The two conductors are made of the same material, but the first is 6 times the length of the second, and 1/5 the radius of the second. The resistance of the second is R₂= 469. Determine the equivalent resistance.

Answer 1

Let ρ is resistivity of material

second resistance $R_2 = 469 \; \Omega$

$\frac{ρl}{\pi R^2} = 469 \\ \frac{ρ \times (\frac{l \times 6}{6})}{\pi (\frac{R}{5})^2 \times 5^2} = 469 \\ (\frac{1}{6} \times \frac{1}{25}) \times \frac{ρ(6l)}{\pi (\frac{R}{5})^2} = 469 \\ (\frac{1}{150}) \times R_1 = 469 \\ R_1 = 469 \times 150 \\ R_1 = 70350 \; \Omega$

The equivalent resistance of parallel resistors

$R_{eq} = \frac{R_1 \times R_2}{R_1+R_2} \\ R_{eq} = \frac{70350 \times 469}{70350 \times 469} \\ R_{eq} = 465.894 \; \Omega$