In the figure, battery B supplies 18 V. Find the charge on each capacitor first

Question

In the figure, battery B supplies 18 V. Find the charge on each capacitor first when only switch S1 is closed. Take C1 = 1.6 uF, C2 = 2.6 uF, C3 =3.7 uF, and C4 = 4.0 uF.

Q1? Q2? Q3? Q4?

Find the charge on each capacitor later when switch S2 is also closed. Q1? Q2? Q3? Q4?

In the figure, battery B supplies 18 V. Find the charge on each capacitor first when only switch S1 is closed. Take C1 = 1.6 uF, C2 = 2.6 uF, C3 =3.7 uF, and C4 = 4.0 uF. Q1? Q2? Q3? Q4? Find the charge on each capacitor later when switch S2 is also closed. Q1? Q2? Q3? Q4?

Explanation / Answer

when s2 is closed

C12 = C1 + C2 = 1.6 + 2.6 = 4.2 micro F

C34 = C3 + C4 = 3.7 + 4 = 7.7 micro F

Cnet = C12*C34/(C12+C34) = 4.2*7.7/(4.2+7.7) = 2.717 micro F

Qnet = V*Cnet

= 18*2.717*10^-6

= 48.92*10^-6 C

Q1 = Qnet*C1/(C1+C2) = 48.92*10^-6*1.6/(1.6+2.6) = 18.63*10^-6 C

Q2 = Qnet*C2/(C1+C2) = 48.92*10^-6*2.6/(1.6+2.6) = 30.29*10^-6 C

Q3 = Qnet*C3/(C3+C4) = 48.92*10^-6*3.7/(3.7+4) = 23.5*10^-6 C

Q4 = Qnet*C4/(C3+C4) = 48.92*10^-6*4/(3.7+4) = 25.42*10^-6 C

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