The effective resistance of a parallel connection that consists of four wires of equal length, equal area of c

Question

The effective resistance of a parallel connection that consists of four wires of equal length, equal area of cross-section and same material is $0.25 \ \Omega$. What will be the effective resistance if they are connected in series?

Accepted Answer

All the wires are identical and of same material so they will have same value of resistance. Let it be $R$. When these are (four) connected in parallel, $R_p = R/4$. Given $R_p = 0.25 \ \Omega$, so $0.25 = R/4$, which gives $R = 1 \ \Omega$. Now these four resistances are arranged in series, $R_s = R + R + R + R = 4R$. Therefore, $R_s = 4 	imes 1 = 4 \ \Omega$.

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