Minute Paper (2/16/04)

• Open circuit vs. short circuit• Current direction: high voltage to low

voltage, except inside the source. • Where do KVL & KCL come from?

– Maxwell eqs. and charge conservation.

Good Lab. Practice

• Make circuits neat• Check the circuit before turning on power, and

turn power if you need change circuit elements.

• Do not touch the circuit with bare hand when power is on.

• Make sure the grounding is good• When using meters, start with large range first• Do not short voltage source or open current

source.

Series Resistors and the Voltage Divider Rule

iiii

RRRi

RiRiRi

vvvV

321

321

332211

3215.1

, i.... ,

:series in resistorsN for general In

5.1

1N1

1

321

N

nn

N

nnEQ

EQ

EQ

vviiRR

RRRR

iRV

• Series Circuit: One branch same current through each resistor.

NRRRR ,......., :resistors seriesa For 21EQ

VR

Rv

VR

Rv

VR

Rv

EQ

EQ

EQ

5.1

5.1

5.1

33

22

11

Voltage Divider:

Example: voltage divider

If you want to use your car battery (12 V) to power your laptop computer which requires 3V power supplier, how would you do it.

3

123

12

21

21

1

11

RR

RR

R

R

Rv

EQ

Practical voltage sources

Ideal voltage source: rs=0

SLS

LLSL

LS

SS

vRr

RRiv

Rr

vi

The output voltage is now depend on the RL

Make rs << RL, so vL vS , independent on RL

Parallel Resistors and the Current Divider Rule

NRRRR ,......., :resistors parallelFor 21EQ

SEQ

SEQ

SEQ i

R

R

R

vii

R

R

R

vii

R

R

R

vi

333

222

111 , , Current Divider:

321

33

22

11

321

321

111

; ;

:KCL

:KVL

RRRvi

R

vi

R

vi

R

vi

iiii

vvvv

S

S

,v.... ,11

:parallel in resistorsN for general In

1111

1N1

1

321

N

nnS

N

n nEQ

EQ

EQS

iivvRR

RRRR

R

vi

•Parallel Circuit: resistors share the same terminal same voltage on each resistor.

Large current though smaller R

Advantage of parallel circuit: a broken branch will not affect other branches

Practical current sources

Ideal current source: rs=∞

SLS

SL

LS

LSEQ

sL

EQL

iRr

ri

Rr

RrR

iR

Ri

The output current is now depend on the RL

Make rs >> RL, so iL iS , independent on RL

Ammeter

• Ammeter: – measure current, – put in series, – The lower the internal resistance is, the better the

meter is

Voltmeter

• Voltmeter: – measure voltage, – put in parallel, – the higher the internal resistance is, the better the meter is.

An example: parallel circuit

There is a circuit break in circuit that supplies power to your kitchen. The circuit break will be triggered if the total current exceeds 25 A. Can you turn on a 1500W toaster, a 1000W dishwasher, a 1000 W microwave oven, and 1000W refrigerator simultaneously?

A

PPPPi refrigmicrowavedishwashertoaster

5.371000100010001500120

1120120120120

.refrigmicrowavedishwashertoaster iiiii

Concept Check

There are three identical batteries rated 1.5V and max. output current is 200 mA.

• If they are connected in series, – what is total output voltage? – What is max. output current?

• If they are connected in parallel, – what is total output voltage? – What is max. output current?

Simple circuit analysis: Apply element combination rules

Example

R

VI