Capacitor c1 and c2 are 4f and 2f respectively are charged as series combination across 100v battery. The two capacitors are disconnected from each other.They are connected +ve plate to +ve plate and -ve plate to -ve plate.calculate the resulting charge on each capacitor

Question

Capacitor c1 and c2 are 4f and 2f respectively are charged as series combination across 100v battery. The two capacitors are disconnected from each other.They are connected +ve plate to +ve plate and -ve plate to -ve plate.calculate the resulting charge on each capacitor

Answer 1

q = c v

same q on each
v1+v2 = 100
q/c1 +q/c2 = 100
q/4 + q/2 = 100
3 q/4 = 100
q =400/3 on each

now same v on each and total charge=800/3 and total c = 6
v = q/c = 800/18 = 44.4 volts

Answer 2

To calculate the resulting charges on each capacitor, we need to use the principle of conservation of charge. According to this principle, the total charge before and after the capacitors are disconnected remains the same.

First, let's calculate the initial charge on each capacitor when they are in the series combination across the 100V battery.

The formula to calculate the charge on a capacitor (Q) is given by Q = CV, where C is the capacitance and V is the voltage applied across the capacitor.

For capacitor C1 with capacitance 4F and voltage 100V:
Q1 = C1 * V1 = 4F * 100V = 400 coulombs

For capacitor C2 with capacitance 2F and voltage 100V:
Q2 = C2 * V2 = 2F * 100V = 200 coulombs

Now, when we disconnect the capacitors and connect them +ve plate to +ve plate and -ve plate to -ve plate, the charges redistribute to reach a new equilibrium.

Since the plates are connected directly, the voltage across both capacitors becomes the same in the new configuration.

To calculate the new charge on each capacitor, we need to determine the equivalent capacitance (Ceq) of the two capacitors in parallel. The formula to calculate the equivalent capacitance is given by:

1/Ceq = 1/C1 + 1/C2

Substituting the values:
1/Ceq = 1/4F + 1/2F
1/Ceq = 1/4F + 2/4F
1/Ceq = 3/4F
Ceq = 4/3 F

Now, we can use the formula Q = CV to calculate the new charges on each capacitor with the equivalent capacitance (Ceq) and the common voltage across them:

For capacitor C1:
Q1_new = Ceq * V = (4/3 F) * 100V = 400/3 coulombs (approx. 133.33 coulombs)

For capacitor C2:
Q2_new = Ceq * V = (4/3 F) * 100V = 200/3 coulombs (approx. 66.67 coulombs)

Therefore, the resulting charge on capacitor C1 is approximately 133.33 coulombs, and the resulting charge on capacitor C2 is approximately 66.67 coulombs.