Answer to Question #267800 in Electric Circuits for Kevin Campbell

Question

 Determine the net capacitance of each of the circuits (a) and (b) shown in the diagram 

below given that C1=1.0pF, C2=2.0pF and C3=4.0pF. 

b. Find the charge on each capacitor in circuit (b) assuming there is a potential difference of 

12.0 V across the circuit.

Answer 1

for circuits (a):

$1/C=1/C_1+1/(C_2+C_3)$

$C=\frac{C_1(C_2+C_3)}{C_1+C_2+C_3}=\frac{2+4}{1+2+4}=6/7$ pF

for circuits (b):

$C=C_1+\frac{C_2C_3}{C_2+C_3}=1+\frac{8}{2+4}=7/3$ pF

$Q_1=C_1U=12$ pC

$Q=CU=7\cdot12/3=28$ pF

$Q_2/C_2+Q_3/C_3=U=12$

$Q_2+Q_3=Q-Q_1=28-12=16$

$(16-Q_3)/2+Q_3/4=12$

$Q_3=-8$ pC

$Q_2=16-Q_3=16+8=24$ pF