Light bulb When switch is closed, bulbs are … Brighter The same Dimmer than the bulb above (?)

When switch is closed, the right bulb will be … Brighter The same Dimmer than the left bulb now (?)

EXAMPLE: What’s the voltage across, and the current thru each resistor? 12V 100  200  (compare with equivalent R method …)

EXAMPLE: What’s the voltage across, and the current thru each resistor?

Electric circuits: Kirchhoff’s Rules start

Electric circuits: Kirchhoff’s Rules start

Electric circuits: Kirchhoff’s Rules start

Electric circuits: Kirchhoff’s Rules start

Electric circuits: Kirchhoff’s Rules start

The height analogy

(weeeee!)

The height analogy

Electric circuits: Kirchhoff’s Rules Rule 1: The sum of voltage drops around a loop is always zero! (Energy conserved)

The voltage divider 1/2 (solve for I ) No numbers yet!

The voltage divider 2/2 (solve for V 1 & V 2 ) No numbers yet!

The voltage divider: Numbers!

Electric circuits: Kirchhoff’s Rules Rule 2: The sum of currents entering a junction must equal the sum of currents leaving it! (comes in = goes out)

Parallel Circuit No numbers yet!

Parallel Circuit Numbers

A not-to-bad example: NY Kirchhoff’s laws step-by-step …

A not-to-bad example: Currents! 1)Guess directions

A not-to-bad example: Currents! 1)Guess directions 2)Use nodes to reduce set

A not-to-bad example: Voltage Loops! Loop ab cd + - -

A not-to-bad example: Voltage Loops! + + ab c d Loop 2

Solve the equations for the currents! No problem here

A not-to-bad example: The Check!

A bad example: + +

I ) Assign currents! + +

+ +

+ +

II ) Look at currents in & out of nodes + +

+ +

III ) Assign voltage differences (drops)

IV ) Loops! Voltage differences must add to zero a bc d

a bc d

V ) Now, solve those currents More space

Now …