Question

Two conducting wires of same material , equal length and equal diameter are first connected in series and then in parallel.compare the equivalent resistance in each cases

Answer 1

Dear Student,

Since the two conducting wires are of same material and are of same length and equal diameter both will be having similar resistance and let it be 'r'.

case 1:when the wires are connected in series:

Then the equivalent resistance R_S = r₁ + r₂ = r + r = 2r $\Omega$ (since r₁ = r₂ = r)

case 2: when the wires are connected in parallel:

Then the equivalent resistance is determined as

$$\begin{gathered} \frac{1}{R_P}=\frac{1}{r_1}+\frac{1}{r_2}=\frac{1}{r}+\frac{1}{r}=\frac{2}{r} \\ or{R}_P=\frac{{\displaystyle r}}{2}\Omega \end{gathered}$$

Then R_S : R_P = $\frac{2r}{{\displaystyle \raisebox{1ex}{$r$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}=\frac{4r}{r}=4:1$

The above result shows that the equivalent resistance for a series circuit consisting of two wires of same material with similar dimensions will be 4 times the equivalent resistance of the same wires when connected in parallel.


Regards