Combination of Resistors: Practice Problem & Solution
Resistances $n$, each of $r \Omega$, when connected in parallel give an equivalent resistance of $R \Omega$. If these resistances were connected in series, the combination would have a resistance in ohms, equal to: (2004)
Solution Explained:
To solve this problem, we apply the core principles of Combination of Resistors. Understanding the underlying formula is key to arriving at the correct answer below:
The equivalent resistance in parallel is $R = \frac{r}{n}$, which implies $r = nR$. The equivalent resistance in series is $R_s = nr$. Substituting the value of $r$, we get $R_s = n(nR) = n^2R$.
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