Module 4, Lecture 5: Direct Current Circuits
Resistors in series and parallel
Series
R eq

R
1

R
2

R
3

...
 n  i

1
R i
1
R eq

Parallel
1
R
1

1
R
2

1
R
3

...
 i n 

1
1
R i
_________ is the same for all 3 resistors.
_________ is the same for all 3 resistors.
(a) (b)
(c)
R eq
= __________
EF 152 2016 Lecture 4-5
(d)
R eq
= __________
1
Equivalent Resistance
EF 152 2016 Lecture 4-5 2

Kirchhoff’s rules
Some circuits cannot be broken down into series and parallel connections
.
Junction Rule – Valid at any Junction I
1

I

0
Use + for in, – for out.

I

Junction- point where 3 or more conductors meet
I
3
I
2
Gustav Robert Kirchhoff
(March 12, 1824 – October 17, 1887)
Loop Rule – Valid for any closed loop

V

0
Loop- any closed conducting path
EF 152 2016 Lecture 4-5 3
Kirchhoff’s rules step-by-step
•
Draw a large diagram
•
Label all quantities (V, R, I for each path), assume a direction for unknown I’s
•
Use junction rule to reduce number of unknown currents.
Use all but one junction. Use + for in, – for out.
•
Choose a closed loop and assume a direction of travel.
Apply Σ V=0 for the loop, be careful with signs
•
Repeat Σ V=0 for other loops until you have enough equations. Be sure to choose loops so all paths are included at least once.
•
Solve simultaneous linear equations.
•
If you get a negative answer, it means the direction is opposite the assumption.
EF 152 2016 Lecture 4-5 4

Example
Find the current in each part of the circuit.
EF 152 2016 Lecture 4-5
Example
5
EF 152 2016 Lecture 4-5 6

Simultaneous equations in TI-83
 MATRX (2 nd x -1 )  EDIT (Select a matrix to edit, then enter)
 Enter dimensions Row x Column
 Enter coefficients, careful with signs REMEMBER: don’t set all eqns= 0.
 Constants go to other side: 2A+3B+4C+5=0  [2 3 4 -5]
 QUIT (back to home screen)
 MATRX  MATH  rref(
 MATRX  select the appropriate matrix
 Last column gives answers in order
Other methods – Excel, Matlab
14 - (2)i6 - (3)i1 = 0
-(2)i6 - (3)i1 = -14
$B$1:$B$6
$C$1:$C$6= $D$1:$D$6
EF 152 2016 Lecture 4-5 7