Question

Two metallic wires made from copper have same length but the radius of wire 1 is half of that wire 2. The resistance of wire 1 is R. If both the wires are joined together in series, the total resistance becomes??

Answer 1

Answer on Question #73253 - Physics / Electric Circuits

Two metallic wires made from copper have same length $l$ but the radius of wire 1 is half of that wire 2. The resistance of wire 1 is $R_0$. If both the wires are joined together in series, the total resistance becomes?

Solution:

The resistance of wire is related with its length $l$ and radius $r$ by formula

$$R = \rho \frac{l}{A} = \rho \frac{l}{\pi r^2}$$

Because the radius of wire 1 is half of that wire 2 ($r_1 = r_2 / 2$) we obtain that

$$R_2 = \frac{R_1}{4} = \frac{1}{4} R_0$$

When both the wires are joined together in series, the total resistance

$$R = R_1 + R_2 = R_0 + \frac{1}{4} R_0 = \frac{5}{4} R_0 = 1.25 R_0$$

Answer: $1.25 R_0$

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