AS Daily A Level Physics question
In a lab, a potential divider is made from two similar metal-film resistors: R1 = 2.0 kΩ (top) and R2 = 1.0 kΩ (bottom) in series across a 9.0 V supply. The output V_out is taken across R2. After a few minutes both resistors warm equally and each increases in resistance by 10%. Which statement about the new V_out is correct?
Answer
The correct answer is D.
Correct: D — It remains at 3.0 V. Both resistors change by the same percentage, so the ratio R2/(R1+R2) stays 1/(2+1) = 1/3, giving V_out = 9.0 × 1/3 = 3.0 V. A It falls to 2.7 V — wrong because this assumes V_out simply follows the reduced current; R2 also increases by 10%, so I × R2 stays the same fraction of the supply. B It rises to 3.3 V — wrong because it treats V_out as proportional to R2 alone, ignoring that the total resistance also increases by 10%. C It falls to 1.5 V — wrong because this assumes the output halves (e.g. if current halved or resistors shared the voltage equally), which is not the case for a 2:1 divider. D Correct as the divider ratio is unchanged when both resistors scale by the same factor.