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Current and the Motion of Charges
-the rate of flow of electrical charge through a
cross-sectional area
I = ΔQ/Δt
(1A = 1 C/s)
I = qnAv
d
, n = # of free charges = (ρN
avog.
)/M
molar
,
v
d
= drift velocity
Resistance and Ohm’s Law
potential drop V = V
a
– V
b
= EΔL
Resistance : ratio of potential drop to the current
R = V/I
(1Ω = 1V/A)
R = ρL/A
-resistance of a conductivity wire
Energy in Electrical Circuits
P = IV = I
2
R = V
2
/R
(1 watt = 1 J/s)
-power dissipated (potential energy loss per unit
time)
in the conducting segment
-electromotive force (emf) supplies energy to a
circuit (volts), has the same equations as V
-charge through a source of emf (battery), PE
increased by ΔQЄ
P = IЄ
-rate at which energy is supplied by the source
V
a,+
– V
b,-
= Є – Ir, r = internal resistance of battery
I = Є/(R + r)
W = QЄ, Q = total charge the battery can deliver
-total energy stored in a battery
Combinations of Resistors
Series: R
eq
= R
1
+ R
2
+ R
3
+…
V = IR
1
+ IR
2
= I(R
1
+ R
2
)
Parallel: R
eq
= (1/R
1
+ 1/R
2
+ 1/R
3
+…)
-1
V = I
1
R
1
= I
2
R
2
-the current divides into each branch proportionally
Kirchhoff’s Rules
1. when any closed loop surface is traversed, the
sum of the changes in potential must = 0
2. at any junction (branch point), the sum of the
currents into the junction must equal the sum of the
currents out of the junction
Single Loop Circuits:
ex.) –IR
1
– Є
2
– Ir
2
– IR
2
+ Є
1
– Ir
1
= 0
Multi-Loop Circuits:
-the ΔV must still sum to 0 for each loop, do the
inner loop then th outer loop
RC Circuits
-contain a resistor and a capacitor
Discharging a capacitor: no battery, switch is closed
and a current flows, current = the rate of decrease of

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