emf, &

produces current

ΔV = & - IR

battery is nearly constant voltage source but the small resistance reduces the voltage

current stays the same, voltage splits

V = V₁+V₂+V₃=IR₁+IR₂+IR₃

R_eq=R₁+R₂+R₃

splits current, voltage stays the same

I=I₁+I₂+I₃

V/R_eq=V/R₁+V/R₂+V/R₃

1/R_eq=1/R₁+1/R₂+1/R₃

Kirchhoff's Rules:

Junction Rule

Loop Rule

JR=sum of the currents entering equals sum fo currents leaving

LR=sum of changes in potential around a closed loop is 0

Charging a battery: emfs in series and batteries not lined up

same voltage across each capacitor

C_eqV = C₁V+C₂V+C₃V=(C₁+C₂+C₃)V

C_eq=C₁+C₂+C₃

all have the same charge

Q/C_eq=Q/C₁+Q/C₂+Q/C₃=Q(1/C₁+1/C₂+1/C₃)

1/C_eq=1/C₁+1/C₂+1/C₃

capacitor charges when switch is closed

voltage and charge increases with time:

V_C=&(1-e^-t/RC)

Q=Q₀(1-e^-t/RC)

capacitor discharges

Q=Q₀e^-t/RC

even small currents are dangerous (10 mA)

voltage can be lethal if you are wet and touching the ground

safest prongs are 3-pronged b/c they have a ground line 

Ammeter (2)

voltmeter (2)

ohmmeter 

galvanometer (2)

measures current, needs low resistance to not interfere with current, connect in series to measure resistance

measures potential, should not effect voltage so resistance must be large, connect in parallel to measure resistance

measures resistance, need a battery to produce current 

 deflection of needle is proportional to current flowing through it, uses torque to measure current

Resistors in Series

Resistors in Parallel

Capacitors in Series

Capacitors in Parallel 

R_eq=R₁+R₂+R₃

1/R_eq=1/R₁+1/R₂+1/R₃

1/C_eq=1/C₁+1/C₂+1/C₃

C_eq=C₁+C₂+C₃

1Pre, 1Sec

3 resistors, 4 Ω each, 4 scenarios and equivalent resistances