A capacitor is charged through a resistor by an ideal battery
PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences
Problem
A capacitor is charged through a resistor by an ideal battery. A data-collection device measures the potential difference ΔVC across the capacitor at regular time intervals and produces the following verbal description of the resulting ΔVC-versus-time graph:
• At t=0 the plotted value is 0V.
• The curve rises steeply at first and then gradually levels off, approaching 12V as t becomes large.
• The value plotted at t=4.0ms is approximately 7.5V.
No other numerical information is provided.
Answer the following questions using only the qualitative and limited quantitative information given.
(a) Explain what feature of the graph indicates that the circuit contains both a resistor and a capacitor rather than only a resistor.
(b) The experimenter claims that t=4.0ms is very close to one time constant for this circuit. Evaluate the validity of this claim using the graph description.
(c) Without making additional measurements, describe how you could estimate from the graph the time at which the capacitor reaches 90 % of its final potential difference. Explain the reasoning behind your estimation method.
(d) Suppose a second trial is performed with a different resistor while keeping the same capacitor. Describe qualitatively how the new ΔVC-versus-time graph would differ if the new resistor has half the original resistance. Address the initial slope, the new time constant, and whether the final potential difference changes.