Electric Circuits

Power Sources

• Power supplies provide both voltage and current.

• Direct Current (DC)– Batteries and AC adapters

• Alternating Current (AC)– Current follows a sine wave.– Ex. Wall outlet

Battery• A source of electric potential due to a

chemical reaction.

Car

bon

Rod

2e

Zinc Container

Zn2+

NH4Cl MnO2

At the Anode

At the Cathode

eaqZnsZn 2)()( 2

OHaqNHsOMn

esMnOaqNH

2332

24

)(2)(

2)(2)(2

Power Supply• Any source of electrical power.

• It supplies both voltage and current

- Electromotive forcer - Internal resistanceR - Load resistance

rR

PowerSupply

Voltage to Load• The voltage supplied to a load is given by

• Ex. What is the voltage supplied by a 9 volt battery, which has an internal resistance of 15 , when a circuit is drawing 250 mA of current?

rIV

Resistor Combos• Series - The same current goes through each

of the resistors.

• Parallel - The same voltage is applied across each of the resistors.

A BR1 R2 R3

A B

R1

R2

R3

321 RRRRS

321

1111

RRRRP

Kirchoff’s Rules1 Sum of the currents entering a junction

equals the sum of the currents leaving a junction.

2 Sum of the changes in potential across all the elements in a closed loop is zero.

Loop Traversal• Voltage across a resistor

– Across a resistor with the current, I·R– Across a resistor against the current, +I·R

• Voltage across a power source– Across an emf source from to +, +– Across an emf source from + to ,

Network Circuit

R1=10 R2=6

R3=8

I1

I3

I2

20V=Va 15V=Vb

+

+

++

+

Node Equation:

Loop Equation:

I1+I3=I2

VaI1R1+I3R3=0

VbI3R3 I2R2 =0

I1+I3=I2

20I1+8I3=0

15I3 I2 =0

Bridge Circuit

R3=12I1R1=15

R2=10 R4=12

R5=5

I5I4

I3

I2

Va=25V

Ia

I1=I2+I5

I3+I5 =I4

I2+I4 =Ia

+2515I110I2 =0

15I15I5 +12I3=010I25I5 12I4=0

RC Circuits• At t = 0s close a switch

on an RC circuit with an uncharged capacitor.

R

C

I

0C

qRi

RCteIti 0)(

RCteQtq 1)(R

I

0

CQ

Max. Current

Max. Charge

Time Constant• Charging Capacitor

• Time Constant, t RCteQtq 1)(

RC

sF 5.0)0005.0)(1000(

0

0.5Q

1.0QCapacitor Charge

• Ex. What is the time constant for an RC circuit with R=1.0k and C=500F?

Discharging Capacitor

• At t = 0s the capacitor is discharged through resistor R.

0C

qRi

RCtQetq )(

IR C

+

0

0.5Q

1.0QCapacitor Charge