Question

Two resistors, when connected in parallel, give a resultant value of 2 ohms. When the same resistors are connected in series, the value becomes 9 ohms. The individual resistances are:

(a) 1 ohm and 1 ohm
(b) 3 ohms and 6 ohms
(c) 4.5 ohms and 4.5 ohms
(d) 5 ohms and 5 ohms

Answer 1

To determine the individual resistance values of two resistors that result in a combined resistance of 2 ohms in parallel and 9 ohms in series, we apply the formulas for parallel and series resistor combinations and solve the system of equations algebraically.

Step-by-step explanation:

The student is asking about the individual resistance values of two resistors given that their combined resistance in parallel is 2 ohms, and in series is 9 ohms. To calculate the individual resistances, we use the formula for parallel and series combinations. For resistors in parallel, the reciprocal of the total resistance (Rp) is equal to the sum of the reciprocals of the individual resistances (1/R1 + 1/R2). The equation is 1/Rp = 1/R1 + 1/R2. For resistors in series, the total resistance (Rs) is simply the sum of the individual resistances R1 + R2.

Given Rp = 2 ohms for the parallel case, and Rs = 9 ohms for the series case, we set up two equations:
1/Rp = 1/R1 + 1/R2 and Rs = R1 + R2. Substituting the known Rp and Rs values, we get 1/2 = 1/R1 + 1/R2 and 9 = R1 + R2. Solving these equations simultaneously (which can be done using algebraic methods such as substitution or elimination), we'll find the values of R1 and R2. These individual resistance values are different from the incorrect option (d) provided in the question, which states both resistors are 5 ohms.