Download Chris Khan 2008 Physics Chapter 21 The flow of electric charge

Chris Khan 2008
Physics Chapter 21

The flow of electric charge from one place to another is known as electric current.
o
o
represents I as a charge flowing in a given time. Unit = C/s = Ampere.
How
many
electrons
pass
through
a
disk
drive
in
4.5
s
when
the
current
is
0.22
A?
.
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A battery uses chemical reactions to produce a difference in electric potential between two ends, or terminals.
When a battery is disconnected from a circuit and carries no current, the difference in electric potential between its terminals is
electromotive force (emf: ε). The emf determines the amount of work a battery must do to move a certain charge around a
circuit.
.
Electrons flow through metal wires with relative ease. Real wires always affect the electrons to some extent, creating a
resistance to their motion. To make electrons move against this resistance, it is necessary to apply a potential difference between
its ends. For a wire with resistance R, the potential difference V necessary to create a current I is given by Ohm’s law:
.
The unit for resistance is volt per amp  the ohm (Ω).
The quantity that characterizes the resistivity of a given material is resistivity, ρ. Resistance also depends on length and crosssectional area (L and A).
o A current of 1.82 A flows through a copper wire 1.75 m long and 1.10 mm in diameter. Find the potential difference
between



the
ends
of
the
fire.
As a wire is heated, its resistivity tends to increase. The bolometer is an extremely sensitive thermometer that uses the
temperature variation in the resistivity of platinum, nickel, or bismuth as a means of detecting temperature changes as small as
0.0001 C.
Electronic devices incorporating temperature-dependent semi-conductors are thermistors.
∆U = (∆Q)V and P = ∆U/∆t  (∆Q)V/∆t and P = IV = I2R = V2/R.
o A battery with emf 12 V is linked to a 545 Ω resistor. How much energy is lost in the resistor in 65 s?

Energy bills are in kWh (kilowatt-hours), which are equal to 3.6 x 106 J.
o A turkey is cooked for 4 hours in a stove that draws a current of 20A operating at a voltage o 220V using energy that
costs
$0.048
per
kWh.
How
much
does
it
cost
to
cook
this
turkey?

Electrical circuits contain a number of connected resistors. For each type of circuit, we calculate the equivalent resistance
produced by a group of individual resistors.
Resistors connected end-to-end are in series. Three resistors R1, R2 and R3 draw the same current as a single resistor, Req, the
equivalent resistor. V1 = IR1, V2 = IR2 and V3 = IR3, so ε = V1 + V2 + V3 = I(R1 + R2 + R3) = IReq. Req = ∑R.
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o
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A circuit of three resistors is connected to a 24 V battery. The current is 0.0320 A. Find R3 when R1 and R2 are given as
250 Ω and 150 Ω respectively.
Also find the potential difference across each R.
Internal resistance, r, of a battery causes the potential difference between the terminals to be less than ε. Therefore, resistance is
r + R.
Resistors connected across the same potential difference are in parallel. The total current is equal to the sum of the currents
through each of the resistors. Since I1 = ε/R1, etc., I = ε(1/Req). 1/Req = ∑1/R.
o
Consider a battery with three resistors of 250 Ω, 150 Ω and 350 Ω in parallel with a 24 V battery. Find the total current
supplied
by
the
battery
and
the
current
running
through
each
resistor.

Combination resistors are combinations of resistors in series and in parallel.
o The battery emf is 12 V and the resistors have a resistance of 200 Ω. Find the current supplied by the battery to this
circuit.
In
the
diagram
shown,
there
is
one
resistor
parallel
to
two
resistors.

The Kirchhoff rules are ways of expressing charge conservation (the junction rule) and energy conservation (the loop rule) in a
closed circuit.
The Junction Rule tells us that a current entering any point in a circuit must equal the circuit leaving that point. At a junction,
where two or more wires meet, entering current is equal to exiting current and therefore entering current minus exiting current
equals zero.
The Loop Rule is when the net change at the end is zero because you return to where you started from.
. The rule can be stated as: the algebraic sum of all potential differences around
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any closed loop in a circuit is zero.
When analyzing a simple circuit, you use both of these rules. Firstly, try the junction rule. The currents going towards the point
you are analyzing are added and the currents going away from it are subtracted. This term you are adding to and subtracting from
is equal to zero. (i.e. if I1 is going in and I2 & I3 are coming out, I1 = I2 – I3) Next, try the loop rule for each section of the current
and then the whole current. If you move towards the current, you are decreasing electric potential and subtract the term. If you
move away from the current, add the term because you are increasing electric potential. Also take ε into account. (i.e. if the loop
passes the battery, then goes in the direction of two currents with resistors, you get ε – I1R – I2R = 0 where the subscripts depend
on what resistors you pass). Set the term equal to zero due to the loop rule. Once you get each of these loop equations, it’s
basically a system of equations problem.
When capacitors are connected in parallel, each has the same ε (potential difference) between its plates. For example, when
charges Q1, Q2 and Q3 are parallel at capacitors C1, C2 and C3, Q1 = C1ε, Q2 = C2ε and Q3 = C3ε. Therefore, the total charge Q =
Q1 + Q2 + Q2 = εC1 + εC2 + εC3 = (C1 + C2 + C3)ε. If an equivalent capacitor is used to replace the three in parallel, the
charge on its plates must be the same as the total charge on the individual capacitors: Q = Ceqε. Comparing this with the last
derivation, we see Ceq = C1 + C2 + C3.
o Two capacitors of 12µF and unknown capacitance C are connected in parallel across a battery with 9 V. The total
energy stored in the capacitors is 0.0115 J.
What is C?
Remember the equation for U.
Remember Q = CV from the last chapter. When three capacitors have the same charge Q, the potential difference for each is:
Since the total potential difference across the three capacitors must equal the emf,
.

In RC Circuits, resistors limit the rate at which charge can flow. Before t = 0, there is no current in the resistor or charge on the
capacitor. At t = 0, the switch is closed and current begins to flow. If there was no resistor, the capacitor would immediately take
on the charge Q = Cε. Charge varies with time according to:
where
and is the time
constant.
o
For current,
.
A circuit consists of a 126 Ω resistor, a 275 Ω resistor, a 182 µF capacitor, a switch and 3 V battery all in series. Initially
the capacitor is uncharged and the switch is open. At time t = 0, the switch is closed. First, what charge will the
capacitor have a long time after the switch is closed. Secondly, at what time will the charge on the capacitor by 80
percent
of
the
value
found
before
this
in
part
A?