To determine which expression correctly represents the parallel combination of resistors, let's analyze the characteristics of resistors in parallel and necessary formulas:
### Concept Explanation:
When resistors are connected in parallel, the total or equivalent resistance ([tex]\(R_{\text{total}}\)[/tex]) can be found using the sum of the reciprocals of the individual resistances. Mathematically, it is expressed as follows:
[tex]\[ \frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} \][/tex]
This formula is derived based on the fact that in a parallel circuit, the voltage across each resistor is the same and the total current is the sum of the currents through each resistor.
### Options Analysis:
- (a) [tex]\( \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} \)[/tex]:
This corresponds to the correct formula for calculating the equivalent resistance in a parallel circuit.
- (d) [tex]\( R_1 R_2 R_3 \)[/tex]:
This expression does not relate to any common method for calculating total resistance in parallel or series circuits. Multiplying the resistances directly as shown in [tex]\( R_1 R_2 R_3 \)[/tex] has no meaningful connection to either configuration.
### Conclusion:
The correct answer is therefore:
- c) both a & b (considering only (a))
Thus, the answer to the question "Which of the following represents the parallel combination of resistors" is:
- 3. c) both a & b
In summary, the representation in option (a) accurately provides the relationship used to compute the total resistance in a parallel circuit by summing the reciprocals of individual resistances. The option (d) does not relate to the method used for parallel resistors. Hence, option (c) is the correct choice, including option (a).
