Three ideal capacitors having capacitances ,

PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

Three ideal capacitors having capacitances C1=0.50 μFC_{1}=0.50\,\mu\text{F}, C2=1.0 μFC_{2}=1.0\,\mu\text{F}, and C3=2.0 μFC_{3}=2.0\,\mu\text{F} are connected in series to an adjustable dc power supply. After a long time the circuit has reached electrostatic equilibrium. (a) Use symbols to derive a general algebraic expression for the ratio ΔV1ΔV2\dfrac{\Delta V_{1}}{\Delta V_{2}} of the potential differences across any two capacitors in a series combination. (b) Without substituting numbers, rank ΔV1\Delta V_{1}, ΔV2\Delta V_{2}, and ΔV3\Delta V_{3} from greatest to least and justify your ranking using your result from part (a). (c) Using your ranking, explain qualitatively which capacitor stores the greatest amount of electric potential energy and why.

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