Solution

ID: past-exam-of-the-physics-2-paper-of-the-university-of-oxford/2014-resit/6/solution

Let denote the capacitance omitted after the word “capacitance” in the source sentence. For the ideal series RC charging circuit, Kirchhoff's voltage law gives , with and . Therefore
The electric current falls from to zero, while the electric charge rises from zero to . Their initial slopes are and , respectively.
Reducing shortens the approach to the relevant final values. Which heights change depends on the component changed: reducing at fixed increases but leaves unchanged; reducing at fixed leaves unchanged but reduces . A shorter time constant alone does not specify both endpoint amplitudes.
Figure 1.
RC charging with the same resistance and two different capacitances
. The reference time is R times the larger capacitance. Reducing capacitance halves the time constant and final charge while keeping the initial current fixed. Details.

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