AS Daily A Level Physics question
A student builds a potential divider with a fixed resistor R1 in series with an adjustable resistor R2 across a 9.0 V supply. With R2 set to 3.0 kΩ, the voltmeter across R2 reads 6.0 V. R1 is left unchanged. If R2 is then set to 1.5 kΩ, what reading is expected across R2?
Answer
The correct answer is A.
Correct: A — 4.5 V. From the first setting, 6.0/9.0 = 2/3, so R1 must be half of R2 (1.5 kΩ); with R2 then set to 1.5 kΩ, R1 = R2, so the 9.0 V splits equally and the meter reads 4.5 V. A: Uses the ratio from the first reading to find R1 = 1.5 kΩ, then equal resistors share the supply equally giving 4.5 V. B: 3.0 V assumes the current stays the same so V across R2 halves with R2, but the total resistance changes so the current does not stay constant. C: 6.0 V ignores that changing R2 changes the share of the supply; the same reading would require keeping the same R2:(R1+R2) ratio. D: 9.0 V is the full supply and would only appear across R2 if R1 were effectively zero or the meter were across the entire supply.