In the circuit below, i = 7.3 Amps, R1 = 2.5Ω and R2 = 1.6Ω. Find Vs in Volts to 2dp.

Question

BlackTom AI · Accepted Answer

Start by analyzing the circuit configuration: the two resistors R1 and R2 appear to be connected in parallel, with the voltage source Vs supplying the entire network and the current i = 7.3 A flowing from the source into the junction that feeds both resistors.

First, compute the equivalent resistance of the parallel branch. For two resistors in parallel, Req = (R1 * R2) / (R1 + R2).
Plugging in R1 = 2.5 Ω and R2 = 1.6 Ω gives Req = (2.5 × 1.6) / (2.5 + 1.6) = 4.0 / 4.1 ≈ 0.9756 Ω.

Next, relate the source voltage to the total current and the equivalent resistance seen by the source. Since the source drives the parallel combination directly, the voltage across the parallel branch is Vs and the current through the source is i = 7.3 A. By Ohm's law for the equivalent resistance, Vs = i × Req.
Thus Vs ≈ 7.3 × 0.9756 ≈ 7.122 V.

For reporting purposes to two decimal places, this result is approximately 7.12 V. If you check the intermediate steps, you should see that the parallel combination provides a reduced resistance compared to either individual resistor, which explains why the calculated Vs is less than what you would get if the resistors were in series or if only a single resistor were present.

In the circuit below, i = 7.3 Amps, R1 = 2.5Ω and R2 = 1.6Ω. Find Vs in Volts to 2dp.

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