Between terminals P and Q lies a capacitor network controlled by a single-pole switch…

PHYSICS · Multi-part · CBSE · Physics · Electrostatic Potential and Capacitance · Electrostatic Potential and Capacitance

Problem

Between terminals P and Q lies a capacitor network controlled by a single-pole switch S that can connect to position 1 or position 2. Position 1 (OPEN): Capacitors

C_{1}=6\,\mu\text{F}

and

C_{2}=3\,\mu\text{F}

are connected in series between P and Q; capacitor

C_{3}=9\,\mu\text{F}

is isolated, having one plate connected to the junction between

C_{1}

and

C_{2}

and its other plate unconnected. Position 2 (CLOSED): The free plate of

C_{3}

is connected to terminal Q, placing

C_{3}

in parallel with

C_{2}

while

C_{1}

remains in series with the

C_{2}

–

C_{3}

branch. Initially, S is in position 1. The network is connected to an ideal 10 V dc source for a long time, after which the switch is moved instantaneously to position 2. (a) Determine the equivalent capacitance between P and Q while the switch is in position 1. (b) Determine the equivalent capacitance between P and Q immediately after the switch is moved to position 2 (assume no time for charge redistribution yet). (c) After the switch has been in position 2 for a long time, calculate the charge that has flowed through the switch during the transition from part (a) to the new steady state. Clearly state how you account for conservation of charge in your reasoning.

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