kirchhoff's Law - The Burns Home Page

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kirchhoff's Law - The Burns Home Page

Practice

In the circuit below, find ε 1, I 2 , I 3 I

e

2

1

3 Equations, 3 Unknowns

12V 4V

Loop 1

1) + (0.5A)(2Ω) + ε 1 - 12V - I 2 (4Ω) = 0

2) + I


2 (4Ω) + 12V - 4V + I 3 (6 Ω )= 0

4Ω Loop 2


3) 0.5A + I 2 = I 3

I 1 =0.5 I 3

11V

e1 4I2

0

11V

e1

41.1V

0

8V

6I3

4I2

0

e1

4.4V

11V

I3 0.5A I I3 0.5A

A 1.1

2

e1

6.6V

8V

6 0. 5A

I 4I

0

0.6A

2 2

8V 3V 6I 4I

0

2 2

11V

10I2

0

I2 1.1A

The “-” on the

currents indicate that

our original direction

guess was wrong

Practice

In the circuit below, find the current in each resistor and the equivalent

resistance of the network of five resistors.

13V

a

I 1


c

I 3


I 4

d




I 2

I 5

b

Practice

This “bridge” network cannot be represented in terms of series and

parallel combinations. There are five different currents to determine, but

by applying the junction rule to junctions a and b, we can determine then

in terms of three unknown currents.

Loop 2

13V

I 1+ I 2

Loop 1

a

I 1

c


Loop 3 1Ω


I 3


I 1 –

I 4 I 3

d


I 2

I 2 + I 3

I 5

b

Using the

current

directions as

guides, we will

define 3 loops

(3 equations

for the 3

unknowns)

Loop 2

13V

+

I 1+ I 2

Loop 1

Practice

Loop 1: V I1 I1 I3


Loop 2:

Loop 3:

a

I 1

c

Loop 3

1Ω 1Ω


I 3


I 1 –

I 4 I 3

13 1W 1W 0


13V I 1W I I 2W 0

2 2 3


I 1W I 1W I 1W 0

1 3 2

d


I 2

I 2 + I 3

I 5

b

This is a set of 3

equations and

three unknowns.

So let’s solve

5

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