CircuitAnalysis

Chapter 18

AP Physics: M. Blachly

Review

2 0 0

V = 3 V

1 0 0

5 0

What is the total resistance of this circuit?

Find the current that flows out of the battery.

What is the power dissipated in the 200 ohm resistor?

A new problem:

2 0 0

V = 3 V

5 0

V = 1 .5 VWhat is the power dissipated in the 200 ohm resistor?

Kirchoff’s Laws

The Basic Idea:

• What goes in must come out.

• If you walk a complete loop around the block, you must end up back where you started.

Restated in terms of current and voltage

• The sum of the currents in any junction must be equal to zero

• The sum of the voltage drops around any closed loop must be zero.

Application to first Problem

2 0 0

V = 3 V

1 0 0

5 0

I 1

I 3

I 2

Kirchoff’s Laws

The sum of the currents in any junction must be equal to zero

• Pick a direction for the current in each branch and label it. Don’t worry if you are wrong: the solution will fix that

The sum of the voltage drops around any closed loop must be zero.

• Going in the direction of your current, the voltage will drop through a resistor. If going opposite I, the voltage will increase.

• Going backwards through a battery will drop the voltage.

Kirchoff’s Results

The application of Kirchoff’s Laws will yield n equations with n unknowns. We can solve these equations by

• Substitution

• Elimination

• Matrix operations.

Equations

1 2 3

2 3

1 3

0

200 100 0

50 100 3

I I I

I I

I I

We can now use K’s laws to find the system of equations that describe our circuit:

Matrices and the Ti-8x

Nice reference for entering matrices on your calculator: • http://www.itc.csmd.edu/mth/ti83/matrix/enter.htm

Followed by one for operations on matrices:• http://www.itc.csmd.edu/mth/ti83/matrix/rref.htm

2 5 1

4

x y

x y

Matrix Representation

1 2 3

1 1 1 0

0 200 100 0

50 0 100 3

I I I C

Matrix Operations

Putting the matrix in Reduced Row Echelon form yields

1 2 3

1 0 0 0.0257

0 1 0 0.0086

0 0 1 0.0171

I I I C

Example 2: Your turn

8

1 2 V

6

I 1

9 V

5

1 0