Two resistors give 2 ohm when joined in parallel and 9 ohm when joined in series. What are the two resistance values?
- 1 ohm and 8 ohm
- 4 ohm and 5 ohm
- 2 ohm and 7 ohm
- 3 ohm and 6 ohm
Show answer and solution
Correct answer: D. 3 ohm and 6 ohm
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_