Which one of the following is the resistance that must be placed parallel with 12Q resistance to obtain a combined resistance of 4Q ?

To find the resistance that must be placed in parallel with a 12Ω resistor to achieve an equivalent resistance of 4Ω, we use the parallel resistance formula: 1/Req = 1/R1 + 1/R2 [c2][t1]. Given Req = 4Ω and R1 = 12Ω, the equation becomes 1/4 = 1/12 + 1/R2. Rearranging to solve for the unknown resistance, we get 1/R2 = 1/4 - 1/12. By finding a common denominator, 1/R2 = 3/12 - 1/12 = 2/12 [t1]. Inverting this result gives R2 = 12/2 = 6Ω [t1]. This confirms that a 6Ω resistor placed in parallel with a 12Ω resistor results in a combined resistance of 4Ω, which is consistent with the principle that the equivalent resistance in a parallel circuit is always less than the smallest individual resistance [t1][t8].

Sources

1. [1] Science , class X (NCERT 2025 ed.) > Chapter 11: Electricity > Activity 11.6 > p. 186