Calculate the output voltage V of the following circuit.

Question

BlackTom AI · Accepted Answer

Voltage divider between 10 V and 4 V yields the node voltage by dividing the 6 V potential difference across R1 and R2 in proportion to their resistances.

1) Relevant concepts
- Series resistors share the same current. 
- The voltage across the series chain equals the difference between the two terminal voltages (10 V − 4 V = 6 V). 
- Voltage division: the voltage across each resistor = I·R, where I = (V_top − V_bottom)/(R1 + R2).

2) Step-by-step reasoning
- Identify top and bottom potentials: V_top = 10 V, V_bottom = 4 V.
- The total voltage across the series resistors is V_total = V_top − V_bottom = 10 − 4 = 6 V.
- The resistors are in series so current I = V_total / (R1 + R2).

3) Calculations (all intermediate steps)
- R1 = 60 Ω, R2 = 30 Ω, so R_total = 60 + 30 = 90 Ω.
- Current I = 6 V / 90 Ω = 0.066666... A = 1/15 A.
- Voltage across R2 (lower resistor) = I · R2 = (1/15 A) × 30 Ω = 30/15 = 2 V.
- Node voltage V (measured relative to the same reference used for 10 V and 4 V) is V_bottom + voltage across R2 = 4 V + 2 V = 6 V.
(Alternatively: voltage across R1 = I·R1 = (1/15)×60 = 4 V, so V = V_top − 4 V = 10 − 4 = 6 V.)

4) Why the correct answer is correct
Because the 6 V difference between the ends is split in the ratio R1:R2 = 60:30 = 2:1, the lower resistor gets one part (2 V) and the upper resistor gets two parts (4 V). Adding the lower resistor’s 2 V to the 4 V reference gives 6 V at the midpoint.

5) Why other options are incorrect
- a. 2 V would be only the voltage across R2, but that is measured above the 0 V reference; it ignores the 4 V bottom reference (so it confuses relative/absolute voltages). 
- b. 4 V is the bottom node value given in the diagram, not the midpoint. 
- d. 8 V would result from an incorrect division (for example, placing more drop on the lower resistor); it contradicts the series current calculation.

6) Conclusion
The midpoint voltage V is 6 V, matching answer c. 6 V.

Calculate the output voltage V of the following circuit.单项选择题

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