Two resistors give 2 ohm when joined in parallel and 9 ohm when joined in series. What are the two resistance values?

1. Write the two conditions from the data given. 2. Series gives $R_1 + R_2 = 9$. 3. Parallel gives $\dfrac{R_1 R_2}{R_1 + R_2} = 2$, so $R_1 R_2 = 2 \times 9 = 18$. 4. Now find two numbers that sum to 9 and have product 18; these are 3 and 6. 5. Check: parallel $= \dfrac{3\times6}{9} = 2\,\Omega$, series $= 9\,\Omega$, both match. 6. Trap B (4,5): sum 9 but product 20, so parallel would be 2.22, not 2. 7. Trap C (2,7): product 14 gives parallel 1.56; trap D (1,8): product 8 gives parallel 0.89. _Source: Samacheer Kalvi (TN SCERT) Class 10 Science, Unit 4 Electricity "Electricity", p.64_