What is the reading on the voltmeter given the following values:Power supply: 15 VoltsR1: 7 OhmsR2: 18 OhmsR3: 18 Ohms

Question

BlackTom AI · Accepted Answer

Voltage across R1 equals the supply voltage times the fraction R1/(R1 + (R2 || R3)). Treat R2 and R3 as two resistors in parallel, that parallel in series with R1, and the voltmeter reads the drop across R1 (it is connected between the top rail and the junction at R1’s bottom).

1) Knowledge points:
- Parallel resistance formula: Rpar = (R2·R3)/(R2 + R3).
- Series total resistance: Rtotal = R1 + Rpar.
- Ohm’s law: I = V / Rtotal; voltage across R1: VR1 = I·R1.
- Ideal voltmeter has very large resistance so it does not appreciably change the circuit.

2) Step-by-step calculation:
- Compute R2 || R3:
  R2 = 18 Ω, R3 = 18 Ω
  Rpar = (18 · 18) / (18 + 18) = 324 / 36 = 9 Ω.
- Total series resistance:
  Rtotal = R1 + Rpar = 7 Ω + 9 Ω = 16 Ω.
- Total current from the 15 V supply:
  I = V / Rtotal = 15 V / 16 Ω = 0.9375 A.
- Voltage across R1 (what the voltmeter reads):
  VR1 = I · R1 = 0.9375 A · 7 Ω = 6.5625 V ≈ 6.56 V.

3) Why this is correct:
The voltmeter is connected across the top node and the junction after R1, so it measures the drop across R1. With R2 and R3 forming a 9 Ω parallel equivalent below R1, the series current is 0.9375 A and the resulting drop across the 7 Ω resistor is 6.5625 V.

4) Why the other choices are incorrect:
- (a) 0.938 V: this matches the total current in amperes (0.9375) when numerically interpreted as volts, not a voltage; it is not the voltage drop across R1.
- (c) 15.0 V: would imply no voltage drop anywhere else (R1 = 0 or open circuit), which is not the case.
- (d) 8.44 V: this is the voltage across the parallel combination R2||R3 (I · 9 Ω = 8.4375 V), not across R1.

Conclusion: The voltmeter reads 6.56 V, which matches the provided correct answer.

What is the reading on the voltmeter given the following values:Power supply: 15 VoltsR1: 7 OhmsR2: 18 OhmsR3: 18 Ohms单项选择题

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