Download Kirchhoff`s junction law.

Circuits
AP Physics 1
A Basic Circuit
 All electric circuits have three main parts
 A source of energy
 A closed path
 A device which uses the energy
 If any part of the circuit is open the device will
not work!
Current
 Electric current is the movement of electric charges though a material.
 Currents are charges in motion, so we define current as the rate, in coulombs per second, at which
charge moves through a wire.
 The unit for current is the Amp, or Ampere (A).
 1 Amp = 1 Coulomb/second
Kirchhoff’s Junction Law
 A junction is a point where a wire
branches.
 For a junction, the law of conservation
requires
 The basic conservation statement, that the
sum of the currents into a junction equals
the sum of the currents leaving, is called
Kirchhoff’s junction law.
Potential Difference
 In order to have current, we have to push our charges.
 In a battery, a series of chemical reactions occur in
which electrons are transferred from one terminal to
another. There is a potential difference (voltage)
between these poles.
 The maximum potential difference a power source can
have is called the electromotive force or (EMF), ε. The
term isn't actually a force, simply the amount of energy
per charge (J/C or V).
 The unit for potential difference is volt (V).
Resistance
 You must continuously apply an EMF to make current flow, which
means that there is something that opposes the flow of charge.
 We call this opposition Resistance (R).
 The unit for resistance is the Ohm, Ω.
 All materials have some resistance, even metals.
 The resistance of a wire is given by the equation to the right.
 Resistivity ρ characterizes the electrical properties of materials.
 Materials that are good conductors have low resistivity. Materials
that are poor conductors (and thus good insulators) have high
resistivity.
 For most circuits in this class, we will consider wires to have zero
resistance (unless otherwise stated).
Resistors
 Often, we intentionally add resistance to a circuit.
 In a toaster oven, we use Nichrome wire because it has a high resistivity for a metal (about
100 times more than copper). Because of this, the wires heat up and toast your bread.
 Resistors are used in circuits like the one below to control the amount of current and the
voltages in a circuit.
Voltage Drops in Circuits
 As current moves through a circuit, it
encounters voltage drops from resistors.
 Each time you pass a resistor, some of the
electrical energy is turned into thermal energy
in the resistor.
 We call this a potential difference, because the
potential changes as you move across the
resistor. Because of this we have to measure
voltage across a resistor, not at just one point.
Kirchhoff’s Voltage Law
 Kirchhoff’s voltage law states that if you travel along any closed loop, the sum of the potential
differences will be zero.
 Each element in the loop (battery, resistor, etc.) creates a potential difference; sometimes they will be
a rise in potential, sometimes they will be a drop in potential.
Ohm’s Law
 For most materials, increasing the amount of
voltage increases the current through the
material.
 Our constant of proportionality between
these two values is the resistance of the
material.
 This formula is referred to as Ohm’s Law.
Electrical Power
 When current runs through a lightbulb or a resistor, it dissipates electrical energy into heat.
 The dissipated electrical power can be calculated using one of the following equations:
 The unit for power is a watt (W), just like in mechanics.
Basic Circuit Components
 Before you begin to understand circuits you need to be able to draw what they look like using a
set of standard symbols understood anywhere in the world.
 For the battery symbol, the long line is considered to be the positive terminal and the short line,
negative.
 The voltmeter and ammeter are special devices you place in or around the circuit to measure the
voltage and current.
Ways to Wire Circuits
 There are 2 basic ways to wire a circuit. Keep in mind that a resistor could be anything (bulb, toaster,
ceramic material…etc)
 Series – One after another
 Parallel – between a set of junctions and parallel to each other
Measuring Current
 To determine the current in the circuit, we
insert the ammeter. To do so, we must
break the connection between the battery and
the resistor.
 Because they are in series, the ammeter and
the resistor have the same current.
 The resistance of an ideal ammeter is zero so
that it can measure the current without
changing the current.
Measuring Voltage
 A voltmeter is used to measure the potential differences in a circuit.
 Because the potential difference is measured across a circuit element, a voltmeter is placed in parallel with
the circuit element whose potential difference is to be measured.
 An ideal voltmeter has infinite resistance so that it can measure the voltage without changing the voltage.
 Because it is in parallel with the resistor, the voltmeter’s resistance must be very large so that it draws very
little current.
Series Circuit
 In a series circuit, the resistors are wired
one after another. Since they are all part of
the same loop they each experience the
same amount of current.
 The sum of the voltages across each resistor
is equal to the total voltage of the battery.
I ( series)Total  I1  I 2  I 3
V( series)Total  V1  V2  V3
Equivalent Resistance in Series
 As the current goes through the circuit, the charges must use energy to get through the resistor.
 Each individual resistor will eat up some electric potential. We call this voltage drop.
V( series)Total  V1  V2  V3 ; V  IR
( I T RT ) series  I1 R1  I 2 R2  I 3 R3
Rseries  R1  R2  R3
Rs   Ri
Example
Calculate the equivalent resistance of the circuit, the
current in the circuit, and the voltage drop across
each resistor.
Parallel Circuit
 In a parallel circuit, we have multiple loops.
So the current splits up among the loops with
the individual loop currents adding to the
total current.
 It is important to understand that parallel
circuits will all have some position where the
current splits and comes back together. We
call these junctions.
 The current going in to a junction will always
equal the current going out of a junction.
I ( parallel)Total  I1  I 2  I 3
Regarding Junctions :
I IN  I OUT
Equivalent Resistance in Parallel
 Notice that the junctions both touch the positive and
negative terminals of the battery. That means you have
the same potential difference down each individual
branch of the parallel circuit. This means that the
individual voltages drops are equal.
V( parallel)Total  V1  V2  V3
I ( parallel)Total  I1  I 2  I 3 ; V  IR
VT
V1 V2 V3
( ) Parallel  

RT
R1 R2 R3
1
1
1
1
 

RP R1 R2 R3
1
1

RP
Ri
Example
Calculate the equivalent resistance of the circuit, the current in each resistor, and
the voltage drop across each resistor.
Complex Circuits
 Combinations of resistors can often be reduced to a single equivalent resistance through a step-by-step
application of the series and parallel rules.
 Once you have found the total resistance of the circuit, you can determine the total current in the
circuit. That current can be used to calculate the voltage drop across each resistor.
Example
Determine the current through each resistor as well as the
voltage drop across each resistor.
Lightbulbs
Lightbulbs
 It is common in introductory circuits to have ranking questions for lightbulb brightness.
 Any time you encounter a question like this, the bulbs will be identical. Because of this, the
bulb that dissipates the most power will be the brightest.
Example
Rank the brightness of each bulb in the circuit. Assume the bulbs are identical.
Example
Rank the brightness of each bulb in the circuit. Assume the
bulbs are identical.
Example
The lightbulbs are identical. Initially both bulbs are glowing.
What happens when the switch is closed?
(A) Nothing.
(B) A stays the same; B gets dimmer.
(C) A gets brighter; B stays the same.
(D) Both get dimmer. A gets brighter;
(E) B goes out.
Example
Initially the switch in the circuit below is open. Bulbs A and B are equally bright, and bulb C is not
glowing. What happens to the brightness of A and B when the switch is closed? And how does the
brightness of C then compare to that of A and B? Assume that all bulbs are identical.