(1) Label all currents

Choose any direction

(2) Choose loop and direction

Must start on wire, not element.

Kirchhoff’s Laws

(3) Write down voltage drops

-Batteries increase or decrease

according to which end you encounter first.

-Resistors drop if going with current.

-Resistors increase if gong against current.

e 1 - I 1 R 1 - I 2 R 2 -e 2 =0

For inner loop

A

R 1 I 1

R 2

E 3

B

E 1 I 2 I 3

E2 R 3

R 5

I4

R 4

Label Choose Write KVR currents loop

or

Find I:

ε 1 - IR 1 - ε 2 - IR 2 = 0

50 - 5 I - 10 -15 I = 0

I = +2 Amps

Practice

e 1 = 50V

A

R 1 =5 W

What if only went from A to B?, Find V B -V A

V B - V A = e 1 - IR 1

= 50 - 25 = 40 Volts

V B - V A = +IR 2 + e 2

= 215 + 10 = +40 Volts

Therefore B is 40V higher than A

e 1 = 50V

A

R 2 =15 W

R 1 =5 W

R 2 =15 W

I

I

B

e 2 = 10V

B

e 2 = 10V

Understanding

Practice

slide 7

Resistors R 1 and R 2 are:

1) in parallel 2) in series 3) neither

Definition of parallel:

Two elements are in parallel

if (and only if) you can make

a loop that contains only

those two elements.

I 1

E 2 = 5 V

I 2

I B

R 1 =10 W

R 2 =10 W

+ -

E 1 = 10 V

Definition of series:

Two elements are in series if (and only if) every loop that

Contains R 1 also contains R 2

Calculate the current through resistor 1.

1) I 1 = 0.5 A

2) I 1 = 1.0 A

3) I 1 = 1.5 A

e IR

0

1 1 1

e1

I1

R

I 1 R 1 =10 W

E 2 = 5 V

I 2 R 2 =10 W

I B

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