Final answer:
The question asks about achieving an equivalent resistance of 4.5 Ω using a combination of resistors. The solution involves applying series and parallel resistor formulas to combine the resistances step by step. The final equivalent resistance is achieved by simplifying the circuit step by step using the rules for combining resistors in series and parallel.
Step-by-step explanation:
To achieve a total equivalent resistance of 4.5 Ω using a combination of resistors, understand the principles of combining resistances both in series and in parallel. When resistors are in series, their resistances add up (Requiv = R₁ + R₂ + R3 + R4). In parallel, the combined resistance is found using the reciprocal formula (1/Requiv = 1/R1 + 1/R2 + ... + 1/Rn). You can simplify complex circuits by combining series and parallel resistors step-by-step.
From the information provided, we know that two resistors in a dashed box have a combined resistance of 4.77 Ω, which can simplify the circuit analysis. Additionally, certain combinations like R4 and R5 are given specific parallel formulas (1/Requiv = 1/R₁ + 1/R5). By understanding which resistors are in series and which are in parallel, we can replace them with their equivalent resistances step by step.
In the given example, R3 and R4 in series can be combined into one resistance of R34, and then this new resistance can be combined with R2 in parallel to get R234. Finally, adding R234 in series with R1 gives us the total equivalent resistance (Req). Utilizing that circuit reductions, such as those represented in Figure 10.15, allows us to gain insight into the equivalent resistance of a more complex network of resistors.
Strategy for solving the problem:
- Combine resistors that are in series.
- Apply the parallel resistor formula for resistors in parallel.
- Repeat the process until you are left with a single equivalent resistance that matches the desired value.
The resistors in parallel can be seen as choices for resistance values that, when combined correctly, meet the total resistance requirement. For example, the combination giving 1.84 Ω likely involves more than two resistors in parallel, while a combination of just two resistors yields a resistance formula of 1/Requiv = 1/Rblue + 1/Rred.
In the context of the question regarding four equal resistors in parallel with a 17V voltage supply, the voltage across each of them remains 17V due to the nature of parallel circuits where the voltage is the same across all parallel components.