In the circuit below, i = 4.3 Amps, R1 = 6.4Ω and R2 = 9.8Ω. Find Vs in Volts to 2dp.

Question

BlackTom AI · Accepted Answer

Ohm’s law (V = I·R) with the equivalent resistance of parallel resistors is the key. The two resistors R1 and R2 are in parallel, so compute their equivalent resistance and multiply by the total current i to get Vs.

1) Relevant concepts
- Parallel resistance: R_eq = (R1·R2)/(R1 + R2).
- Ohm’s law for the source: Vs = i · R_eq, where i is the total current supplied by the source.

2) Step-by-step reasoning and calculations
- Given: i = 4.3 A, R1 = 6.4 Ω, R2 = 9.8 Ω.
- Compute numerator R1·R2 = 6.4 × 9.8 = 62.72 (Ω^2).
- Compute denominator R1 + R2 = 6.4 + 9.8 = 16.2 Ω.
- Equivalent parallel resistance:
  R_eq = 62.72 / 16.2 = 627.2 / 162 = 3.871604938... Ω (carrying sufficient digits for accuracy).
- Now apply Ohm’s law:
  Vs = i · R_eq = 4.3 × 3.871604938... = 16.647901233... V.
- Round to two decimal places: Vs ≈ 16.65 V.

3) Why this answer is correct
- The circuit shows the two resistors directly in parallel across the source, so the source sees the parallel combination. Using the correct formula for parallel resistance and then V = I·R gives the correct source voltage. The arithmetic above yields 16.6479 V, which rounds to 16.65 V to two decimal places.

4) Why other answers would be incorrect
- A common mistake would be to add resistances (treating them as series) giving R = 16.2 Ω and Vs = 4.3·16.2 = 69.66 V — clearly wrong for the shown parallel connection.
- Rounding too early or using insufficient precision in R_eq can shift the second decimal (e.g., using 3.873 gives 16.66 V); proper intermediate precision yields the correct 16.65 V.

Conclusion: The calculated source voltage to two decimal places is 16.65 V, matching the provided answer.

In the circuit below, i = 4.3 Amps, R1 = 6.4Ω and R2 = 9.8Ω. Find Vs in Volts to 2dp.数值题

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