Curent, Resistance ,Directcurrent Circuits
• Electric current
• The current is the rate at which charge
flows through this surface
• Suppose ΔQ is the amount of charge that
flows through an area A in a time interval
Δt and that the direction of flow is
perpendicular to the area. Then the current
I is equal to the amount of charge divided
by the time
• I= Δ Q/Δt
• SI C/s=A (Ampere)
• Resistance and Ohm’s Law
• Resistance is the ration of the voltage
across the conductor to the current:
• R = ΔV/ I
• SI units :1V/A=1Ω (Ohms)
• Ohm’s Law: the resistance remains
constant over a wide range of applied
voltage or currents:
• ΔV =IR
• A resistor : is a conductor that provides a
specified resistance in an electric circuit
• Materials that obey Ohm’s law, are called
ohmic
• Materials having resistance that changes with
voltage or current are nonohmic (Ex: dioded = a
circuit element that acts like one way valve for
current)
• The resistance is proportional to the conductor’s
length l and inversely proportional to its crosssectional area A:
• R =ρ l/A
• Ρ –resistivity of the material (ct. of
proportionality) SI unit: Ω m
• Electrical energy and power
• The rate at which the system loses potential
energy as the charge passes through resistor is
equal to the rate at which the system gains
internal energy in the resistor.
• (ΔQ/ Δt) ΔV =I ΔV
• Power P- the rate at which energy is
delivered to the resistor:
• P =I ΔV
• P =I2R = ΔV2/R
• SI: kilowatt-hour
• 1kWh =(103W)(3600s) =3.6x106J
• Sources of EMF (electromotive force)- a “
charge pump” that forces electrons to move in a
direction opposite the electrostatic field inside
the source
• The emf Σ of a source is the work done per unit
charge (SI unit: V)
• ΔV =Σ –Ir
• Σ = the terminal voltage when the current is zero
(open circuit voltage)
• ΔV= IR (R- the external resistance)
• Σ =IR +Ir; I =Σ/ (R+r)
• IΣ =I2R + I2r if r<<R (the power delivered by the
battery is transferred to the load resistance)
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Resistors in series
ΔV = IR1 +IR2 =I(R1+R2)
ΔV = I Req
IReq = I(R1+R2)
Req =R1+R2
Req =R1+R2+….
The equivalent resistane of a series
combination of resistors is the algebraic
sum of the individual resistances and is
always greatter than any individual
resistance
• Resistors in parallel
• The potential differences across resistors are the
same because each is connected directly across
the battery terminals
• Because charge is conserved, the current I that
enters point a must equal the total current I1+I2
leaving that point
• I =I1+I2
• I1=ΔV /R1 ; I2=ΔV /R2 ;
• I =ΔV /Req ; 1/Req = 1/R1 +1/R2
• The inverse of the equivalent resistance of two
or more resistors connected in parallel is the
sum of the inverses of the individual resistances
and is always less than the smallest resistance
in the group
• Kirchhoff’s Rules:
• 1. The sum of the urrents entering any
jonction must equal the sum of the
currents leaving that junction (junction
rule)
• 2. The sum of the potential differences
across all the elments around any closed
circuit loop must be zero (loop rule)
• a) if the resistor is traversed in the
direction of the current, the charge in
electric potential across the resistor is -IR
• b) If a resistor is traversed in the direction
opposite the current, the charge in electric
potential across resistors is +IR
• c) if a source of emf is traversed in the
direction of the emf (from – to +) the
charge in electric potential is +Σ
• d) if a source of emf is traversed in the
direction opposite the emf, the charge in
electric potential is -Σ
• Problem solving strategy:
• 1. Assign labels and symbols to all the known
and unknown quantities
• 2. Assign directions to the currents in each part
of the circuit
• 3. Apply the junction rule to any junction in the
circuit
• 4. Apply Kirchhoff’s loop rule, to as many loops
in the circuit as are needed to solve for the
unknowns
• 5. solve the equations
• 6. Check your answers by substituting them into
the original equations