DC CIRCUITS

Releasing Electric Energy – Current

●

Allow separated

+

and

–

charges to come back

together by making an electric “

circuit

”

–

i.e. a path connecting the + and – charges

●

Electric current

(symbol:

I

)

–

The flow of

+

charge from one location to another

–

Units

: Amperes (

A

) = Coulombs / second (

C/s

)

●

Current occurs when there is a “

voltage drop

” (

ΔV

)

–

Difference

in voltage between one location and another

–

Often due to a battery, capacitor, or generator

–

KE of moving charges can be used → electronic devices

+

–

Resistance and Ohm's Law

●

Resistor

–

Device that converts current to another form of energy

●

Resistance

–

Defined by “Ohm's Law”

–

Units

: Measured in Ohms (

Ω

)

–

Depends on

shape

of object and

resistivity

of material (

ρ

)

R

=

Voltage

drop

Current

R

=

V

I

R

=

L

A

“

Ohm's Law”

Limits of Ohm's Law

●

Ohm's Law fits most materials well

–

Although

resistivity (

ρ

)

depends strongly on

temperature

●

Counter-examples: “Non-ohmic” materials

–

Superconductors

→ R=0(

!

) below certain temperature

–

Semiconductors

→ R can be changed drastically

Batteries and EMF

●

Ideally, a battery has constant

Δ

V

through its life

–

But

real

batteries are not ideal:

–

They have an “internal resistance” (

r

– notice lower case)

●

In general:

–

Where

ε

is called “

electromotive force

”

–

ε

is the “ideal” voltage of the battery

●

The more current a battery puts out:

–

The more voltage is “eaten” by internal resistance

A

B

V

AB

=

−

Ir

Power in Electric Circuits

●

Electric power used by resistor:

–

Units

: Measured in Watts (

W

)

–

Given by any of 3 equivalent expressions:

●

Resistors convert energy into a variety of forms:

Power

=

Energy

used

time

1,000 – 10,000 W

1000 W (avg. for 24 hrs)

P

=

VI

P

=

I

2

R

P

=

V

2

R

1 – 500 W

If not converted to

other “useful”

forms, the power

must be dissipated

as

heat

energy

Health Risks of Electric Currents

●

Burns

–

Electric power is dissipated as heat, which burns tissue

●

Convulsions

–

Current can cause violent muscle contractions → injury

●

Heart issues

–

Current can disrupt the heart's natural electrical rhythm

–

Current as little as 0.1 Amps can be lethal in this way

Circuit Diagrams

●

Used to describe circuits abstractly

●

Symbols

:

Battery

Resistor

Capacitor

Switch

+

V (or

ε

)

R

C

S

Voltmeter

V

Ammeter

A

Ground (V=0)

Circuit “Rules”

1) Any two points connected

by wires only

have same

V

–

So:

V

A

= V

B

→

Δ

V

AB

= 0

2) At an intersection of wires:

current in = current out

–

“

Kirchoff's Current Rule” →

I

1

+ I

2

= I

3

3) Sum of

ΔV

's

around closed loop must be

zero

–

“

Kirchoff's Voltage Rule” →

ΔV

battery

– ΔV

resistor

= 0

+

A

B

I

1

I

2

I

3

Connecting Circuit Elements

●

Series

(one end connected to next element)

–

Current

must be same for each element

●

Parallel

(both ends connected to next element)

–

ΔV

must be the same for each element

–

If a circuit element is removed / off:

–

The rest of the circuit is unaffected

●

Other

(both series and parallel – or neither)

+

+

Equivalent Resistance & Capacitance

Resistors

Series:

Parallel:

Capacitors

Series:

Parallel:

I

total

=

I

1

=

I

2

R

1

R

2

V

total

=

V

1

V

2

R

eq

=

R

1

R

2

R

1

R

2

V

total

=

V

1

=

V

2

I

total

=

I

1

I

2

1

R

eq

=

1

R

1

1

R

2

C

1

C

2

Q

total

=

Q

1

=

Q

2

V

total

=

V

1

V

2

1

C

eq

=

1

C

1

1

C

2

V

total

=

V

1

=

V

2

Q

total

=

Q

1

Q

2

C

eq

=

C

1

C

2

C

1

C

2

RC Circuits

●

Stored energy in a capacitor

–

Is released using a resistor (“

discharging

” the capacitor)

–

Of course, the capacitor must be “

charged

” first

Charging a capacitor

Current flows until capacitor voltage

equals the battery's

ε

+

q

=

Q

final

1

−

e

−

t

RC

Discharging a capacitor

Current flows until capacitor has zero

charge (and zero voltage)

q

=

Q

0

e

−

t

RC

=

RC

“

time constant”

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