1

DC circuits, Kirchhoﬀ

`

s Laws

CHM6158C -‐ Lecture

2

•

Alternating Current (AC), Direct Current (DC)

•

DC Circuits

•

Resistors

•

Kirchhoff

`

s Laws

2

Electric current

Movement of electrons in a conductor

Examples of good conductors:

•

copper

•

aluminum

•

silver

Cable enclosed with an insulating

material (e.g. polyethylene)

http://www.hydroquebec.com/learning/images/quest-

ceque/i_schema_atome.gif

Units

:

Charge (Q)

Coulomb (C)

1.603x10

-19

C

Voltage (V)

Volts (V)

1 V = 1 J/C

Current (I)

Amperes (A)

1 C/s

Power (P)

Watts (W)

P = IV

At what speed does

electricity propagate?

A current of 100 mA can be lethal !

3

Conduc@vity

Conductivity = measure of a material

`

s ability to conduct an electrical current

Inverse: Resis@vity vs. Resistance

silver > copper > aluminum

Resistivity

= measure of how strongly a material opposes the flow of electrical

current (units:

Ω

m) (inherent of material)

J

E

ρ

Magnitude of electric field (V / m)

Magnitude of current density (A / m

2

)

Resistance

= measure of how strongly a material opposes the flow of electrical

current (units:

Ω

) (dependent on cross-section and length of material)

I

V

R

OHM

`

s LAW

Strange units –

why?

4

Alterna@ng current (AC)

AC (alternating current): movement of electric charges periodically changes

direction

Mains power: 110 V

RMS

, 60 Hz

Actually, this is the root-mean-square (RMS) voltage = V

0-p

/sqrt(2)

5

Direct current (DC)

Current flowing in

one

direction

(typically static or changing slowly)

Exact nature of voltage depends

on power source

6

DC circuit

e.g. battery

Can think of this as movement of

electrons from source potential

–

to

+

around the circuit

However, convention in electronics, current

moves from + to – in the circuit. This can be

imagined as a movement of the charge as

l

holes

z

(i.e., absence of electrons), which

is especially useful for semi-conductors

(diodes, transistors).

What will determine the amount of

current that will move through the

circuit for a given voltage?

7

Ohm

`

s Law

Convention

: current flows from + to – in the circuit

What is voltage here?

e.g. +3 V and -3V

What is voltage here?

Voltage drop

across

the resistor

What is the

current in the

circuit?

8

Resistors: facts

Made of a compound, film or

resistance wire (e.g. nickel/chrome)

Important consideration: what is the

maximum dissipative power (W) that a

resistor can tolerate?

P = IV = I*(IR) = I

2

R

Resistors will burn out if the dissipative

power is too great!

Symbols:

9

Resistor nota@on

4 bands: 5% accuracy

10

Kirchhoﬀ

`

s Laws

1.

At any node in an electrical circuit, the

sum

of the

currents

flowing into that node is equal to the sum of the currents flowing

out of that node. (= conservation of charge)

⇒

For a

parallel

circuit of N resistors, the total current

I

into the

junction equals the sum of currents (I

1

+ I

2

+ I

3

+ …. + I

N

= I

total

)

⇒

For a

series

circuit of N resistors, the sum of the voltage

drops (IR

1

+ IR

2

+ IR

3

+ …. + IR

N

= V

source

)

I

t

I

1

I

2

2.

The directed sum of the electrical potential differences around

a closed circuit is zero (= conservation of energy)

11

Resistors in series

1.5 V battery

Current is the

same

everywhere

in the circuit.

)

(

2

1

2

1

R

R

I

IR

IR

IR

V

total

in

By analogy for N resistors in

series:

)

(

...

1

2

1

∑

N

N

total

in

R

I

IR

IR

IR

IR

V

What can this principle

be useful for?

12

Resistors in parallel

Voltage drop across each resistor identical, but current is

depends on resistance R.

In this case, total current = sum of currents

2

1

I

I

I

in

2

1

V

V

V

in

2

2

1

1

R

V

R

V

R

V

total

in

Know that

∑

N

i

total

R

R

1

1

1

In general:

What will happen when

one resistor has a much

higher value than the other

one?

13

Digital mul@meter (DMM)

Can measure resistances, voltage and

current (AC and DC).

N. B. In Lab Unit 1, will become familiarized with

measuring DC voltages.

If measure voltage, what do we want internal

resistance of the multimeter to be?

……………………………………

If measure current, what do we want internal

resistance of the multimeter to be?

………………………………………..

Why would you

NEVER

connect multimeter in

current-reading mode to

measure between 0 and

+1.5 V?

14

Equivalent circuits

3

2

3

,

2

1

1

1

R

R

R

1

R

2

,

3

1

2

0

1

4

0

1

1

3

.

3

!

)

(

67

.

0

)

(

3

.

13

9

)

(

15

A

V

R

V

I

total

Ω

?

?

15

Voltage divider

In this case, would it be safe to

measure the

current

between

0.8 V

AB

and 0.6 V

AB

for

instance?

What consequences would this

have for the circuit?

What would happen to the circuit if

we measured the

voltage

between

0.8 V

AB

and 0.6 V

AB

?

16

Examples

What is the current in this circuit?

Assume all resistors are

equivalent (100

Ω

), what is the

total resistance of these circuits?

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