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Electric Circuits
Chapter 18 
Series Circuits

To find the equivalent resistance for
resistors in series, use
Req = R1 + R2 + R3 + …
Series Circuits

Voltage is shared…
current is the same
through each resistor

Vtot = V1 + V2 + V3…

IRtot = IR1 + IR2 + IR3

IRtot = I(R1 + R2 + R3)
Parallel Circuits

To find the equivalent resistance for
resistors in parallel, use
1/Req = 1/R1 + 1/R2 + 1/R3 + …
Parallel Circuits

Voltage is the same in each
resistor, but current is
shared…current branches
Itot = I1 + I2 + I3 + …

V/Req =V/R1 + V/R2 + V/R3

1/Req = 1/R1 + 1/R2 + 1/R3

Example

What is the equivalent resistance of
three resistors, R1 = 1.0 Ω; R2 =
2.0 Ω and R3 = 3.0 Ω in a) series
and b) parallel.
What current will be delivered by a
12 V battery in each circuit?
Series and Parallel
Combinations




Determine which groups are in series and
which are in parallel.
Reduce the circuit by treating equivalent
resistances as individual resistors
Find the total current delivered in the
circuit
Expand the reduced circuit back to the
actual circuit by reversing the steps…
Example

See page 597… Find the current in
each resistor.
Kirchhoff’s Rules

Kirchhoff’s rules are used to solve
multi-loop circuits…

A point where three or more wires
are joined is called a junction.

A path connecting two junctions is
called a branch.
Kirchhoff’s Rules
Kirchhoff’s Rules

Kirchhoff’s First Rule – the sum of
currents at any junction is zero. The sum
of currents entering and leaving a
junction is zero.

Kirchhoff’s Second Rule - the sum of
potential differences across all elements
of a closed loop is zero. The sum of
voltage rises and drops in a loop must be
zero.
Example

Two resistors are connected in parallel
and then connected in series with a third.
A battery completes the circuit.
a) which resistor carries the most
current?
b) If R1 = 6.0 Ω, R2 = 3.0 Ω and R3 =
10.0 Ω and the battery’s terminal voltage
is 12.0 V, find the current in each resistor
and the voltage across each resistor.
Sign Conventions in
Kirchhoff’s Rules
When using the loop theorem, when
you follow the loop in the direction
of voltage increase, V>0. When
you follow the loop in the opposite
direction, V<0.
 When you follow the loop across a
resistor in the direction of current,
V<0. In a direction opposite to
current, V>0.

Sign Conventions in
Kirchhoff’s Rules
Example

Series and parallel calculations
cannot be used in Figure 18.10 page
603. Instead, use Kirchhoff’s Rules
to generate three equations. Use
algebra to solve three equations for
three unknowns: I1, I2 and I3.
RC Circuits

Circuits with Resistors and Capacitors are called
RC circuits.

Initially the capacitor is uncharged so the circuit
acts like a voltage – resistor circuit

As the capacitor charges, the charge
accumulating on it (and associated negative
voltage) reduces the current.

As charge on capacitor increases, current in the
circuit decreases.
RC Circuits

Vc = V0[1 - e-t/RC]
Where Vc is the voltage
across the capacitor and
V0 is the battery
voltage.

Note t = 0 and t
approaches infinity.

Also note t = RC
RC Circuits

I = I0 e-t/RC

I0 is initial current in
the circuit

Note t = 0 and t
approaches infinity.

Also note t = RC
RC Circuits – Time Constant

Time Constant τ = RC

When t = τ = RC,
Vc = 0.63 V0
I = 0.37 I0
Charging and Discharging

In some
circuits, the
capacitor is
continuously
charged and
discharged.

For
discharge,
V=V0e-t/RC
Example

In many cameras the built in flash gets its
energy from that stored in a capacitor.
The capacitor is charged using long life
batteries V=9.0V. Once the bulb is fired,
the capacitor must recharge quickly
through an internal RC circuit. If the
capacitor has a value of C = 0.100F, what
must the resistance be so the capacitor is
charged to 80% of maximum in 5.0 sec?
Ammeters and Voltmeters



An ammeter measures current
A voltmeter measures voltage
Both devices contain a coil of wire attached to a
needle inside a magnetic field…a Galvanometer.
Due to electromagnetic induction, the presence
of a current will cause a needle to deflect.
Ammeters and Voltmeters are galvanometers.
Ammeters

Because an ammeter
measures current in a circuit
loop, all current should travel
through the ammeter.
Therefore it is placed in
series with the circuit.

In order that all current
travels through the ammeter,
it should have a very small
resistance.

An ammeter measures
current through a circuit
element.
Voltmeter

A voltmeter measures a
potential difference across
a circuit element.

It is placed in parallel to a
circuit element.

In order that the
voltmeter not affect the
current (and therefore the
voltage) in a circuit
element, it should have a
very high resistance.
Household Wiring
In series, if one element goes out all
other elements go out. All elements
share the total voltage.
 In parallel, if one element goes out
the other elements will remain on.
All elements have the same voltage.
 Is a house wired in series or in
parallel?

Household Wiring

Household wiring involves three
wires… the ‘hot’ wires have 120V
difference between them. These are
black and white.

The third wire is a ground wire –
connected directly to the ground. It
has ZERO potential.
Circuit Breakers

If current in a circuit is too great, the wire or
circuit elements can overheat and cause a fire.

Recall extra ‘branches’ in a parallel arrangement
reduces the overall resistance. Extra appliances
have the same effect…. Current therefore
increases.

Circuit breakers limit the amount of current in a
loop. The circuit is broken if current is
exceeded.
Homework
Read Section 18.5
 Do # 80, 81, 90 – 93, 97 – 100
 Prepare for exam on Chapt 17, 18


Cathode is negative… it is the
electrode at which reduction (gain of
electrons) occurs