Suppose the three-capacitor network: C1=1uF , C2=4uF and C3=2uF is connected acr

Question

Suppose the three-capacitor network: C1=1uF , C2=4uF and C3=2uF is connected across a 12 V battery.

Follow these steps to find the charge on each capacitor.

A). Use the equivalent Capacitance to find the Charge Supplied by the Battery.

B.) Note that the charge supplied by the battery equals the charge Q3 on the capacitor C3. (WHY?)

----> Use this fact to compute the potential difference V3 across C3

C.) Compute the potential difference across the other two capacitors.

D.) Use your answer from part (c) to find the charge stored on each of the C1 and C2.

------> Note: Q1 and Q2 aren't the same.

Explanation / Answer

A.)

1/5 + 1/2 = 1/C

1/C = 7/10

C = 10/7 uF

Q = VC = 12(10/7) =120/7 uC

B.)

V3 = Q/C3 = (120/7)/(2) = 60/7 V

C.)

V =12 - V3 = 12 - 60/7 = ( 84 - 60 )/ 7 = 24/7 volts

D.)

Q1 = VC1 = (24/7) (1) = 24/7 uC

Q2 = VC2 = (24/7) (4) = 96/7 uC

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