Final answer:
The total resistance of 1k, 2.2k, and 3.3k ohm resistors in parallel is approximately 569 ohms. The calculation involves the sum of reciprocals of each resistor's value and demonstrates why total resistance in a parallel circuit is less than the smallest individual resistor.
Step-by-step explanation:
Total Resistance of Parallel Resistors
Calculating the total resistance in a parallel circuit involves a different approach compared to a series circuit. In parallel, the reciprocal of the total resistance (1/Rtotal) is equal to the sum of the reciprocals of each individual resistance (1/R1 + 1/R2 + 1/R3 ...). For the given resistors of 1kΩ (1.00 x 103 ohms), 2.2kΩ (2.20 x 103 ohms), and 3.3kΩ (3.30 x 103 ohms), we calculate as follows:
1/Rtotal = 1/(1 x 103) + 1/(2.2 x 103) + 1/(3.3 x 103)
1/Rtotal = 1/1000 + 1/2200 + 1/3300
1/Rtotal = 0.001 + 0.0004545 + 0.0003030
1/Rtotal = 0.0017575
Therefore, Rtotal = 1/0.0017575 ≈ 569 ohms, which is the total resistance of the resistors when connected in parallel.
The total resistance of resistors in parallel will always result in a value that is less than the smallest individual resistor in the network. Understanding Ohm's law in a parallel circuit is critical to solving such problems.