Calculate the output voltage V of the following circuit.

Question

BlackTom AI · Accepted Answer

Voltage divider rule gives the node voltage directly: V = Vin * R2 / (R1 + R2).

1) Relevant concepts:
- Series resistors share the same current. 
- The voltage divider formula for a node between R1 (top) and R2 (bottom) with the bottom tied to ground is Vout = Vin · (R2 / (R1 + R2)).
- Ohm’s law: V = I·R, and total series current I = Vin / (R1 + R2).

2) Step-by-step reasoning and calculations:
- Given: Vin = 15 V, R1 = 300 Ω (top), R2 = 600 Ω (bottom, to 0 V). The node V is the voltage above ground at the junction (i.e., across R2).
- Total resistance: R_total = R1 + R2 = 300 Ω + 600 Ω = 900 Ω.
- Series current: I = Vin / R_total = 15 V / 900 Ω = 1/60 A = 0.0166667 A (16.67 mA).
- Voltage across R2 (which equals the node voltage V relative to ground): V = I · R2 = (1/60 A) · 600 Ω = 600/60 V = 10 V.
- Alternatively using the divider formula: V = 15 V · (600 / 900) = 15 · (2/3) = 10 V.

3) Why the correct answer is correct:
- The bottom resistor is twice the top resistor, so the junction sits two-thirds of the way down from the top supply toward ground. Two-thirds of 15 V equals 10 V. Both Ohm’s law and the divider formula give 10 V.

4) Why other options are incorrect:
- 5 V would be the voltage drop across R1 (I·R1 = 0.016667·300 = 5 V), not the junction to ground.
- 6 V and 3 V do not match the calculated divider ratio (600/900)·15 = 10 V and are therefore incorrect.

Conclusion: The output voltage V is 10 V, matching choice d.

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

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