In the circuit below, consisting of a battery and several capacitors, some quant

Question

In the circuit below, consisting of a battery and several capacitors, some quantities are known and some are not. The capacitors were completely uncharged before the battery was attached and we are considering the static situation. (Be sure to keep at least 3 sig. figs. in your answer for all parts of this problem.)

Q1= 8.4 × 10-6 C

C1= 5.9 × 10-6 F

C2= 3 × 10-6 F

Energy stored

on C2 is W2= 4.4 × 10-6 J

A) What is the potential difference across C1?

V1 = V     

B) What is the potential difference across C2 ?

V2 = V     

C) What is the potential difference across C3?

V3 = V     

D) What is the charge Q3 on capacitor C3?

Q3 = C     

Q1= 8.4 × 10-6 C

C1= 5.9 × 10-6 F

C2= 3 × 10-6 F

Energy stored

on C2 is W2= 4.4 × 10-6 J

Explanation / Answer

Given

Q1= 8.4 × 10-6 C

C1= 5.9 × 10-6 F

C2= 3 × 10-6 F

Energy stored

on C2 is W2= 4.4 × 10-6 J

here C2,C3 are in parallel and the combination is in series with C1

and we know that if capacitors in series combination the charge is same across each capacitor and

if capacitors in parallel combination the potential difference is same across each capacitor and

so the potential difference across C2,C3 is same that is V2= V3

the combination of C2,C3 is in series with C1 so the charge will be same across C1 and (c2+C3)

A) What is the potential difference across C1, V1 = ?

Q1 = C1*V1 ==> V1 = Q1/C1 = (8.4*10^-6 /(5.9*10^-6) V = 1.424 V

B) What is the potential difference across C2 , V2 = ?

energy stored is U = 0.5*C*V^2

given W2 = 4.4*10^-6 J = 0.5*C2*V2^2

4.4*10^-6 = 0.5*3*10^-6*V2^2

V2 = 1.713 V

C) What is the potential difference across C3, V3 = ?

here C3,C2 are parallel to each other so the potential difference is also same that is  

V3 = 1.713 V

D) What is the charge Q3 on capacitor C3, Q3 = C?

from Q = C*V ==> Q3 = C3*V3 =

from charge Q1 = Q2+Q3

Q3 = Q1-Q2 Q1-C2*V2

Q3 = 8.4*10^-6 - 3*10^-6*1.713 C

Q3 = 3.261*10^-6 C

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