Question

Four resistances of 16 ohms each are connected in parallel. Four such combinations are connected in series. What is the total resistance?

Answer 1

When four resistors of 16 Ω each are connected in parallel, the effective resistance of the combination can be obtained as:
$$\begin{gathered} \frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+\frac{1}{R_4} \\ \mathrm{or}\frac{1}{R}=\frac{1}{16}+\frac{1}{16}+\frac{1}{16}+\frac{1}{16} \\ \mathrm{or}\frac{1}{R}=\frac{4}{16} \\ \mathrm{or}\frac{1}{R}=\frac{1}{4} \\ \mathrm{or}R=4\mathrm{\Omega } \end{gathered}$$
The effective resistance of combination is 4 Ώ.
When four such combinations are connected in series, the effective resistance becomes:
R = R₁ + R₂+ R₃ + R₄
R = 4 Ώ + 4 Ώ + 4 Ώ + 4 Ώ = 16 Ω