Question

Let us be 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 the radius of the second. The resistance of the second is R2 = 469Ω. Determine the equivalent resistance.

Answer 1

The equivalent resistance of the two cylindrical conductors connected in parallel is 466 ohm.

Resistance

Resistance is a measure of the opposition to flow of electric current. It is measured in ohms.

It is given by the formula:

$R=\rho\frac{l}{A} \\\\where\ l=length,A=area,\rho=resistivity$

Given that R₂ = 469 ohm, hence:

$R_2=\rho\frac{l_2}{A_2} \\\\469=\rho\frac{l_2}{\pi r_2^2}$

But l₁ = 6l₂, r₁ = (1/5)r₂, hence:

$R_1=\rho \frac{l_1}{A_1}=\rho *\frac{6l_2}{[\pi (1/5)r_2]^2} =150 * \rho \frac{l_2}{[\pi r_2]^2}=30*469=70350\ ohm$

The equivalent resistance (R) is:

$R=\frac{R_1R_2}{R_1+R_1}=\frac{469*70350}{469+70350} =466\ ohm$

The equivalent resistance of the two cylindrical conductors connected in parallel is 466 ohm.

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