Discussion
The equivalent resistance of the following network shown in figure between the points A and B is
In the figure, a 10 Ω resistor and a 30 Ω resistor are connected in parallel, and this pair is in series with a 2.5 Ω resistor between A and B; a cell is connected across A and B.
Answer: B
The equivalent resistance is 10 ohm.
First combine the parallel pair, then add the series resistor:
\[ \begin{aligned} R_{p} &= \frac{10 \times 30}{10 + 30} = 7.5\ \Omega \\ R_{AB} &= 7.5 + 2.5 = 10\ \Omega \end{aligned} \]
12.5 ohm comes from adding 10 and 2.5 and ignoring the 30 ohm branch, and 30 ohm or 15 ohm come from treating the parallel pair wrongly. A quick check: two resistors in parallel always give less than the smaller of them, so the pair must be below 10 ohm.
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