P222 Ex#2 Part II 1) First, second and third initially uncharged capacitors (hav

Question

P222 Ex#2 Part II 1) First, second and third initially uncharged capacitors (having respective capacitance C,.C, and C,) are connected to a potential source (e) as shown in the circuit of Figure IA. After static equilibrium occurs, the first and third capacitors are carefully removed from the circuit (without discharging) and connected as shown in Figure 1B with a switch that allows the positive plate of C, to be connected to the positive plate of C,. The switch is closed and equilibrium is eventually reestablished. In terms of quantities that do not extend beyond the list of (c,, G,C, and ), derive expressions for: a) the final state potential across the first capacitor of the circuit of Figure 1B long after the switch is closed. b) The total charge that flows through the switch from Ci to C G Ci C1 Figure IB C2 Figure IA

Explanation / Answer

Q3 = C3 e

Q1 = (e C2 C1)/(C1 + C2)

after long time, both capacitors will have same voltage across them.

then Applying charge conservation,

(C1 + C3) V = C3 e + (e C1 C2)/(C1 + C2)

V = (C1 C3 + C2 C3 + C1 C2)e / ((C1 + C2)(C1 + C3)) ......Ans(a)

(b) charge flowed = Q3 - Q

= C3 e - C1 (C1 C3 + C2 C3 + C1 C2)e / ((C1 + C2)(C1 + C3))

= ( C1 C1 C3 + C1 C3 C3 + C1 C2 C3 + C2 C3 C3 - C1 C1 C3 - C1 C2 C3 - C1 C1 C2) e / ((C1 + C2)(C1 + C3))

= (C1 C3 C3 + C2 C3 C3 - C1 C1 C2)e / ((C1 + C2)(C1 + C3))

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