Combination of Resistors: Practice Problem & Solution
Five resistors, each of resistance \(R\) are connected in series to an ideal battery. When these resistors are connected in parallel to the same battery, the current through the battery is increased \(n\) times. The value of \(n\) is
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 series is \(R_s = 5R\) and in parallel is \(R_p = \frac{R}{5}\). Since current \(I = \frac{V}{R_{eq}}\), we have \(\frac{I_p}{I_s} = \frac{R_s}{R_p} = \frac{5R}{R/5} = 25\). Thus, \(n = 25\).
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