DC Circuits

AP Physics

Chapter 18

DC Circuits

19.1 EMF and Terminal Voltage

The Electric Battery

EMF – electromotive force – the potential difference between the terminals of a source when no current flows to an external circuit ()

19.1

The Electric Battery

A battery will have an internal resistance (r)

So there is a potential drop due to the current that travels through the cell

So the actual potential across the terminals of a cell will be

This is called the terminal

voltage

19.1

IrVc

IrEV

DC Circuits

19.2 Resistors in Series and in Parallel

Resistors in Series and in Parallel

When resistors are place in a single pathway

They are said to be in

series

A schematic would look

like this

19.2

Resistors in Series and in Parallel

The current in a series circuit is the same throughout the circuit

The potential across the source of EMF is equal to the sum of the potential drops across the resistors

19.2

nT IIII ....21

nT VVVV ....21

Resistors in Series and in Parallel

Since potential can be defined as

We can rewrite the equation for potential as

19.2

IRV

nT VVVV ....21 nneqT RIRIRIRI ....2211 neq RRRR ....21

Resistors in Series and in Parallel

When resistors are place

in a multiple pathways

They are said to be in parallel

A schematic would look like this

19.2

Resistors in Series and in Parallel

The potential difference in a parallel circuit is the same throughout the circuit

The current through the source of EMF is equal to the sum of the current through the resistors

19.2

nT VVVV ....21

nT IIII ....21

Resistors in Series and in Parallel

Since current can be defined as

We can rewrite the equation for potential as

19.2

R

VI

nT IIII ....21 n

n

eq

T

R

V

R

V

R

V

R

V....

2

2

1

1 neq RRRR

1....

111

21

Resistors in Series and in Parallel

Circuits that contain both series and parallel components need to be solved in pieces

This circuit contains20 resistors in series25 resistors and load series to each

other and parallel to the 40 resistor 19.2

DC Circuits

19.3 Kirchoff’s Rules

Kirchoff’s Rules

Circuits that are a little more complex

We must use Kirchoff’s rules

Gustov Kirchoff

They are applications of the

laws of conservation of

energy and conservation

of charge 19.3

Kirchoff’s Rules

Junction Rule – conservation of charge

At any junction, the sum of the currents entering the junction must equal the sum of all the currents leaving the junction

19.3

321 III

Kirchoff’s Rules

Loop Rule – the sum of the changes in potential around any closed pathway of a circuit must be zero

For loop 1

19.3

03255 31 VIIV

Kirchoff’s Rules

Steps

1. Label the current in each separate branch with a different subscript (the direction does not matter, if the direction is wrong, the answer will have a negative value)

2. Identify the unknowns and apply V=IR

3. Apply the junction rule (at a in our case) so that each current is in at least one equation

19.3

I1 I2I3

0321 III

Kirchoff’s Rules

Steps

4. Choose a loop direction (clockwise or counterclockwise)

5. Apply the loop rule (again enough equations to include all the currents)

a. For a resistor apply Ohm’s law – the value is positive if it goes in the direction of the loop

b. For a battery, the value is positive if the loop goes from – to + (nub to big end) 19.3

I1 I2I3

Kirchoff’s Rules

Steps

We’ll do the two inside loops

6. Combine the equations and solve

19.3

I1 I2I3

021343111 RIERIRIE

0232433 ERIRIE

DC Circuits

19.5 Circuits Containing Capacitors in Series and in Parallel

Circuits Containing Capacitors

19.5

For a parallel set of

capacitors – the total

charge is the sum of

the individual charges

In all parallel circuits – the potential across each branch is the same as the total

nT QQQQ ..21

nT VVVV ..21

Circuits Containing Capacitors

19.5

The equivalent capacitance is the value of one capacitor that could replace all those in the circuit with no change in charge or potential

Since

And

We combine and get

nT QQQQ ..21

CVQ

nnTeq VCVCVCVC ..2211 neq CCCC ..21

Circuits Containing Capacitors

19.5

Series capacitors

The magnitude of the charges is the same on each plate

nT QQQQ ..21

Circuits Containing Capacitors

19.5

The total potential is the sum of the potential drops across each capacitor

We then use that equation and the equation for capacitance

We get

nT VVVV ..21

C

QV

n

n

eq

T

C

Q

C

Q

C

Q

C

Q..

2

2

1

1 neq CCCC

1..

111

21

DC Circuits

19.6 RC Circuits-Resistors and Capacitors in Series

RC Circuits

19.5

Used

windshield wipers

timing of traffic lights

camera flashes