Part A: Calculate the charge on capacitor on C 1. Part B: Calculate the potentia

Question

Part A: Calculate the charge on capacitor on C1.

Part B: Calculate the potential difference across capacitor on C1.

Past C: Calculate the charge on capacitor C2.

Past D: Calculate the potential difference across capacitor C2.

Part E: Calculate the charge on capacitor C3.

Part F: Calculate the potential difference across capacitor C3.

Part G: Calculate the charge on capacitor C4.

Part H: Calculate the potential difference across capacitor C4.

Part I: Calculate the potential difference between points a and d.

Explanation / Answer

Given that :

C1 = C2 = C3 = C4 = 4.90 uF

C1 and C2 are in series and their series combination is given as

C12 = C1 C2 /(C1 + C2)

inserting the values

C12 = (4.9) (4.9)/(4.9 + 4.9)

C12 = 2.45 uF

C12 and C3 are in parallel and their parallel combination is given as

C123 = C12 + C3 = 2.45 + 4.9 = 7.35 uF

C123 and C4 are in series and their series combination is given as

C1234 = C123 C4 /(C123 + C4 ) = (7.35) (4.9)/(7.35 + 4.9) = 2.94 uF

total charge coming from the battery is given as

Q1234 = C1234 Vab = 2.94 x 29 = 85.3 uC

C4 is in series with battery and in series charge remain same

hence

Q4 = Q1234 = 85.3 uC

V4 = potential difference across C4 = Q4/C4 = 85.3/4.9 = 17.4 Volts

V3 = Voltage across C3 = Vab - V4 = 29 - 17.4 = 11.6 Volts

Q3 = charge in C3 = C3 V3 = 4.9 x 11.6 = 56.84 uC

C1 and C2 are in series , hence charge in them will be same

Q1 = Q2 = Q1234 - Q3 = 85.3 - 56.84 = 28.5 uC

V1 = poential difference across C1 = Q1 /C1 = 28.5 /4.9 = 5.82 Volts

V2 = poential difference across C2 = Q2 /C2 = 28.5 /4.9 = 5.82 Volts

Part A: Calculate the charge on capacitor on C1. : 28.5 uC

Part B: Calculate the potential difference across capacitor on C1. 5.82 Volts

Past C: Calculate the charge on capacitor C2.  28.5 uC

Past D: Calculate the potential difference across capacitor C2. 5.82 Volts

Part E: Calculate the charge on capacitor C3. 56.84 uC

Part F: Calculate the potential difference across capacitor C3. 11.6 Volts

Part G: Calculate the charge on capacitor C4.   85.3 uC

Part H: Calculate the potential difference across capacitor C4.   17.4 Volts

Part I: Calculate the potential difference between points a and d. 11.6 Volts

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