Question

Show how you would connect two 4 ohm resistors to produce a combined resistance of (a) 2 ohms (b) 8 ohms.

Answer 1

(a) Case 1
Connecting two 4 Ω resistors in parallel combination:
$$\begin{gathered} \frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2} \\ \frac{1}{R}=\frac{1}{4}+\frac{1}{4} \\ \frac{1}{R}=\frac{2}{4} \\ \frac{1}{R}=\frac{1}{2} \\ R=2\mathrm{\Omega } \\ \mathrm{Thus}\mathrm{we}\mathrm{get}\mathrm{a}2\mathrm{\Omega }resistor. \\ \mathrm{We}\mathrm{should}\mathrm{connect}\mathrm{two}4\mathrm{\Omega }\mathrm{in}\mathrm{parallel}\mathrm{to}\mathrm{get}\mathrm{a}\mathrm{resistance}\mathrm{of}2\mathrm{\Omega }. \end{gathered}$$

(b) Case 2
Connecting two 4 Ω resistors in series combination:
R = R₁ + R₂
R = 4 $\mathrm{\Omega }$ + 4 $\mathrm{\Omega }$ = 8 $\mathrm{\Omega }$
Thus, we will get an 8 Ω resistor.
We should connect two 4 $\mathrm{\Omega }$ resistors in parallel to get a resistance of 8 $\mathrm{\Omega }$.