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Helpful Circuit Stuff

goalkeeper0

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Circuits with resistors:

In series:

Req=R1+R2+R3+R4+...

I=I1=I2=I3=I4=...

V=IR1+IR2+IR3+IR4+...

In parallel:

1/Req=1/R1+1/R2+1/R3+1/R4+...

I=I1+I2+I3+I4...

V=V1=V2=V3=V4=...

Note: Replacing resistors in parallel with one resistor of equivalent total resistance is very useful when analyzing circuits

Circuits with capacitors:

In series:

1/Ceq=1/C1+1/C2+1/C3+1/C4+...

Q=Q1=Q2=Q3=Q4=... (Conservation of charge)

V=V1+V2+V3+V4+...

In parallel:

Ceq=C1+C2+C3+C4+...

Q=Q1+Q2+Q3+Q4... (Conservation of energy)

V=V1=V2=V3=V4=...

After a long time, a capacitor acts like an open spot in the circuit; current through the section of the circuit with the capacitor= 0 A

RC Circuits:

Time constant=RC, or Greek letter tau

I=-dQ/dt

When a resistor and capacitor are in parallel, voltage drop across resistor=voltage drop across capacitor.

When a resistor and capacitor are in series, current is the same through the resistor as through the capacitor.

Charging RC Circuit: Current decreases over time. Charge on capacitor and potential drop across capacitor increase over time.

*In the long run,VC=VT (V-terminal=V-capacitor)

*I=(VT/R)e-t/RC

*Q=Qf(1-e-t/RC)

*Qf=CVT

Discharging a capacitor: Current flows from the positive plate of capacitor to the negative plate and through the resistor. Current, charge, and voltage decrease over time.

*I=I0e-t/RC

*Q=Q0e-t/RC

*I0=V0/R=Q0/(RC)

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