Calculate the effective resistance of the circuit given the following values:R1: 8.8 OhmsR2: 4 OhmsR3: 5.5 OhmsR4: 6.3 OhmsGive your answer to 2 decimal places without units ( For example: 3.45 )

Question

BlackTom AI · Accepted Answer

R2 and R3 are connected in parallel between the node after R1 and the node before R4, so find their parallel equivalent first, then add R4 (series with that parallel pair) and finally add R1 (series with the whole right-hand branch).

1) Relevant concepts:
- Series resistances add: R_series = R_a + R_b + ...
- Parallel resistances add via reciprocals: 1/R_par = 1/R_a + 1/R_b + ...

2) Step-by-step calculation:
- Given: R1 = 8.8 Ω, R2 = 4.0 Ω, R3 = 5.5 Ω, R4 = 6.3 Ω.
- Compute reciprocal sum for R2 and R3:
  1/R2 = 1/4.0 = 0.25
  1/R3 = 1/5.5 ≈ 0.1818181818
  Sum = 0.25 + 0.1818181818 = 0.4318181818
- Equivalent of R2 || R3:
  R23 = 1 / 0.4318181818 ≈ 2.317073171
- Add R4 in series with that parallel: R_right = R23 + R4
  R_right = 2.317073171 + 6.3 = 8.617073171
- Add R1 in series with the whole right-hand branch:
  R_total = R1 + R_right = 8.8 + 8.617073171 = 17.417073171

3) Rounding to two decimal places:
- R_total ≈ 17.42

4) Why this is correct:
- The circuit topology shows R2 and R3 connected between the same two nodes, so they are parallel. R4 is clearly on the single path from that right node to the supply, so it is in series with the parallel combination; R1 is in series with everything on the left. The arithmetic follows directly from series/parallel combination rules.

5) Common incorrect interpretations:
- Treating R4 as parallel with R2/R3 (or combining R1 in parallel) would yield a different value; those are wrong because the schematic shows R4 on the single right-hand branch after the parallel pair, not sharing the same two nodes as R2/R3.

Confirmed final answer (two decimals, no units): 17.42

Calculate the effective resistance of the circuit given the following values:R1: 8.8 OhmsR2: 4 OhmsR3: 5.5 OhmsR4: 6.3 OhmsGive your answer to 2 decimal places without units ( For example: 3.45 )数值题

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