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Capacitors and Dielectrics (IN PARALLEL (V_T=V_1=V_2=V_3, 1/R_eq =1/R_1…
Capacitors and Dielectrics
CAPACITANCE
Q=CV
the capacitance of parallel plate capacitor
IN PARALLEL
V_T=V_1=V_2=V_3
1/R_eq =1/R_1 +1/R_2 +1/R_3
C_eq= C_1+C_2+C_3
Q_total=Q_1+Q_2+Q_3
I_total=I_1+I_2+I_3
IN SERIES
1/C_eq =1/C_1 +2/C_2 +3/C_3
I_total=I_1=I_2=I_3
Q_total=Q_1=Q_2=Q_3
v_total=V_1+V_2+V_3
ENERGY STORED
C=Q^2/2C
U=1/2 CV^2
U=1/2 QV
U=1/2 ε_° E^2
CHARGING
i=ε/R e^(-t/RC)
τ=RC
DISCHARGING
i=-I_° e^(t/RC)
CAPACITANCE WITH DIELECTRIC
C=KC
°=K 〖Aε〗
°/d
E= Q/(Aε_° )
V=ED=Qd/(Aε_° )
E=Q/(4πε_° r^2 )
C=〖Aε〗_°/d