First slide

Capacitors and capacitance

Question

Three large plates are arranged as shown. How much charge will flow through the key k if it is closed?

Moderate

A

$5 Q / 6$
B

$4 Q / 3$
C

$3 Q / 2$
D

none

Solution

$q_{1} + q_{2} = 2 Q$
$V_{AB} = V_{AC} or \frac{q_{1}}{C_{1}} = \frac{q_{2}}{C_{2}}$
$\frac{q_{1}}{q_{2}} = \frac{C_{1}}{C_{2}} = 2 or q_{1} = 2 q_{2}$
Solving, we get $q_{1} = \frac{4 Q}{3}, q_{2} = \frac{2 Q}{3}$
Charge flown through k is
$- \frac{Q}{2} - (- q_{1}) = - \frac{Q}{2} + \frac{4 Q}{3} = 5 Q / 6$

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