Study the circuit below carefully.What is the value of R4 given the following values:Cell voltage: 20Current from the cell: 1.52Resistance R1: 18Resistance R2: 18Resistance R3: 14Give your answer to 2 decimal places.

Question

BlackTom AI · Accepted Answer

Total circuit resistance is R_total = V / I = 20 / 1.52 = 250/19 ≈ 13.15789474 Ω.

Key concept: identify node connections. The center vertical wire ties the midpoint of the top pair to the midpoint of the bottom pair, so R1 and R3 are connected between the same two nodes (left rail and center node) and are therefore in parallel; likewise R2 and R4 are in parallel between the center node and the right rail. Those two parallel groups are then in series across the cell.

1) Compute the left parallel group (R1 || R3):
R1 = 18 Ω, R3 = 14 Ω
R_left = (18·14) / (18 + 14) = 252 / 32 = 63/8 = 7.875 Ω

2) Let R_right = equivalent of R2 || R4 = (R2·R4) / (R2 + R4) = (18·R4) / (18 + R4).

3) Series sum equals total:
R_total = R_left + R_right
250/19 = 63/8 + (18·R4)/(18 + R4)

4) Solve for R4. First compute R_right required:
R_right = 250/19 − 63/8
Common denominator 152: (2000 − 1197)/152 = 803/152

So (18·R4)/(18 + R4) = 803/152.

Cross-multiply:
18·R4 · 152 = 803 · (18 + R4)
2736·R4 = 803·18 + 803·R4
2736·R4 − 803·R4 = 14454
1933·R4 = 14454
R4 = 14454 / 1933 ≈ 7.4776 Ω

Rounded to two decimal places: R4 = 7.48 Ω.

Why this is correct and not the alternate interpretation: a common mistake treats the top two resistors as one series branch and the bottom two as another series branch in parallel; that topology would give R4 ≈ 6.74 Ω, which does not match the circuit wiring shown (the center node ties midpoints together, producing the parallel pairs described above).

Conclusion: R4 = 7.48 Ω, which matches the provided answer.

Study the circuit below carefully.What is the value of R4 given the following values:Cell voltage: 20Current from the cell: 1.52Resistance R1: 18Resistance R2: 18Resistance R3: 14Give your answer to 2 decimal places.数值题

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