# ∑ Resistors in series and parallel Equivalent Resistance Kirchhoff’s rules

```Resistors in series and parallel
Series
Equivalent Resistance
Parallel
n
Req = R1 + R2 + R3 + ... = ∑ Ri
i =1
n
1
1
1
1
1
= +
+
+ ... = ∑
Req R1 R2 R3
i =1 Ri
2
EF 152 Fall, 2009 Lecture 4-7
Kirchhoff’s rules
EF 152 Fall, 2009 Lecture 4-7
Kirchhoff’s rules step-by-step
Loop Rule
Junction Rule
∑V = 0
∑I = 0
1.
2.
3.
4.
5.
6.
7.
8.
9.
Sign convention for junctions:
Use + for in, - for out
I1+I2-I3=0, I3=I1+I2
EF 152 Fall, 2009 Lecture 4-7
3
4
Draw a large diagram
Label all quantities (V, R, I for each path), assume a direction for unknown I’s
Identify unknown values
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 ΣV=0 for the loop, be careful with signs
Repeat ΣV=0 for other loops until you have enough equations. Be sure to
chose 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 Fall, 2009 Lecture 4-7
5
Example
Solutions – Excel, Matlab, TI-83
Find the current in each part of the circuit and the equivalent
resistance of the network.
Microsoft Office
Excel 2007 Workbook
6
EF 152 Fall, 2009 Lecture 4-7
R-C circuits
τ = RC ________________ or
__________________
Lower-case i, q, v mean ___________________
Charging q = CE (1 − e − t /( RC ) ) = Q f (1 − e −t /( RC ) ) Discharging q = Q0e −t /( RC )
Capacitor dq E −t /( RC )
Capacitor
dq − Q0
−t /( RC )
dt
=
EF 152 Fall, 2009 Lecture 4-7
R
e
7
Applications
R-C stands for _____________________
i=
EF 152 Fall, 2009 Lecture 4-7
= I 0e
i=
dt
=
RC
e −t /( RC ) = I 0 e −t /( RC )
8
EF 152 Fall, 2009 Lecture 4-7
9
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