Potential Difference Between Two Points — Question 4

Question 4

An open switch can support the full source voltage while the resistor drop vanishes

An ideal source E and resistor R are in series with an open switch between contacts C and D. There is no leakage, capacitance transient, or meter loading. D is connected to the source negative terminal.

1. Find steady current, resistor voltage and VC-VD.

2. Find these quantities after an ideal switch is closed and explain where the voltage drop moves.

Question 4 - Solution

An open switch can support the full source voltage while the resistor drop vanishes

(a) Method and calculation

$$I_{\mathrm{open}}=0,\quad V_R=I_{\mathrm{open}}R=0.$$$$V_C-V_D=E.$$

(b) Interpretation and further calculation

$$I_{\mathrm{closed}}=E/R,\quad V_R=E.$$$$V_C-V_D=0\quad\text{across the closed ideal switch}.$$

Physical check

Zero current does not imply zero voltage everywhere; an open gap can carry a finite potential difference.