Three resistors of magnitudes 12 Ω, 15 Ω and 20 Ω are connected in (i) series and (ii) parallel. Calculate the combined resistance in each case.

Magnitude of the resistances, 

R₁ = 12 Ω, R₂ = 15 Ω, R₃ = 20 Ω 

(i) Equivalent in series in series, R_s = R₁ + R₂ + R₃
                                                     = 12 + 15 + 20
                                                     = 47 Ω.
ii)

$$\begin{gathered} Equivalent resis\tan ce in parallel combination,\frac{1}{{\mathrm{R}}_{\mathrm{p}}} = \frac{1}{{\mathrm{R}}_1}+\frac{1}{{\mathrm{R}}_2}+\frac{1}{{\mathrm{R}}_3} \\ = \frac{1}{12}+\frac{1}{15}+\frac{1}{20} \\ =\frac{12}{60} \\ = \frac{1}{5} \end{gathered}$$
 ${\mathrm{R}}_{\mathrm{p}} = 5\mathrm{\Omega }.$