A laboratory power supply is suddenly connected to an initially uncharged capacitor…
PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences
Problem
A laboratory power supply is suddenly connected to an initially uncharged capacitor through a fixed resistor. You are interested only in the qualitative behavior—not precise numerical values—of the voltage across the capacitor during the first several time constants of the charging process.
(a) On axes of voltage (vertical axis) versus time (horizontal axis), sketch the expected shape of the capacitor-voltage curve from the instant the circuit is completed until the circuit reaches steady state. Clearly label the following on your sketch: the origin t=0, the point corresponding to one time constant t=τ, and a point that represents a time long compared to the time constant t≫τ. Do not include numerical scales.
(b) Describe how the slope of your curve changes between t=0 and t=τ, and explain the physical reason for that change in slope.
(c) Explain why the voltage approaches a limiting value as t≫τ, and identify what physical quantity in the circuit determines that limiting value.
(d) Suppose the same experiment were repeated with a resistor of twice the original resistance but the same capacitor. Describe—in words—how each of the following features of your sketch in part (a) would change, if at all:
(i) the initial slope at t=0,
(ii) the time-axis location of the point labeled t=τ, and
(iii) the long-time limiting voltage.