Two capacitors, one of 5 μF and the other of 8 μF, connected in parallel, are charged with a 12 volt battery. The battery is then disconnected, and while the capacitors remain connected in parallel, a dielectric with constant 2 is inserted between the plates of the 8 μF capacitor. What is the voltage across this capacitor after the dielectric is inserted?
Given
capacitors c1 = 5 μF and c2 = 8 μF,
battery potential difference v = 12 V
battery disconnected and
dielectric constant k = 2, inserted between the plates of capacitor c2
we know that if the dielectric material of constant k
placed between the plates of capacitor , the capacitance increases
by k times
and potential will decreases by k times
and Q = C*V
V = Q/C
as the battery disconnected then the charge on each plate is constant (does not change)
Q1 = c1*v = 5 μF*12 = 60 μF
Q2 = c2*v = 8 μF*12 = 96 μF
after the battery disconnected
v1 = Q1/c1 = 60/5 = 12 V
v2 = Q2 /(kc2) = 96/(2*8) = 6 V
it would be redistributed (because they are in parallel) then the potential across each capacitor is 9 V
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