In the circuit below, i = 3.3 Amps, R1 = 1.5Ω and R2 = 8.4Ω. Find Vs in Volts to 2dp.

Question

BlackTom AI · Accepted Answer

Ohm’s law and equivalent resistance for parallel resistors give the needed result: Vs = i × R_eq where R_eq is the parallel combination of R1 and R2.

1. Relevant concepts
- Ohm’s law: V = I·R.  
- For two resistors in parallel: R_eq = (R1·R2)/(R1 + R2) or 1/R_eq = 1/R1 + 1/R2.  
The circuit shows the source driving a current i through the parallel pair, so the source voltage equals the product of the source current and the equivalent resistance of the parallel network.

2. Step-by-step reasoning and calculations
- Given: i = 3.3 A, R1 = 1.5 Ω, R2 = 8.4 Ω.  
- Compute the reciprocal sum: 1/R1 = 1/1.5 = 0.6666667 (s⁻¹); 1/R2 = 1/8.4 = 0.11904762 (s⁻¹).  
- Sum: 1/R_eq = 0.6666667 + 0.11904762 = 0.78571429 (s⁻¹).  
- Invert to get R_eq: R_eq = 1 / 0.78571429 = 1.27272727 Ω. (Alternatively R_eq = (1.5·8.4)/(1.5+8.4) = 12.6/9.9 = 1.27272727 Ω.)

3. Final voltage calculation (all intermediate arithmetic shown)
- Vs = i × R_eq = 3.3 A × 1.27272727 Ω = 4.2 V (more precisely 4.19999999 V).  
- Rounding to two decimal places: Vs = 4.20 V.

4. Why this is correct
- The source sees the two resistors as a single equivalent resistor since they are connected in parallel across the source; Ohm’s law then directly gives the source voltage from the known current and equivalent resistance.

5. Other options
- Not applicable (no alternative choices provided). Any other numeric value would contradict Ohm’s law and the computed equivalent resistance.

Conclusion: The computed source voltage is Vs = 4.20 V, which matches the provided answer.

In the circuit below, i = 3.3 Amps, R1 = 1.5Ω and R2 = 8.4Ω. Find Vs in Volts to 2dp.Numerical

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