Consider the circuit shown in the figure. The switch has been in position 1 for a long time. Answer following questions:
(a) Find current through 2R.
(b) Find potential difference across the capacitor.
(c) At t = 0 the switch is moved to position 2. What current flows through the capacitor immediately after the switch is placed to position 2?
(d) Draw a graph of current Vs time for the current through the capacitor after the switch is moved to position 2. Indicate the time on the graph when the current becomes 37% of its value immediately after the switch is put to position 2

Question

G1 Physics · Accepted Answer

Image In position 1 for a long time the capacitor is open. The R and 2R branch carries V/(3R), so voltage at the switch node is 2V/3 relative to the lower rail; capacitor has this voltage. After switching to position 2, it discharges through the relevant resistance, giving exponential current. At one time constant the current is e⁻¹ ≈ 0.37 of its initial value.