Voltage and Current
Division Rules
Dr.-Eng. Hisham El-Sherif
Electronics and Electrical Engineering Department
ELCT708: Electronics for Biotechnology
1
Objectives
• To apply the voltage and current
division rules.
Dr.-Eng. Hisham El-Sherif
Electronics and Electrical Engineering Department
ELCT708: Electronics for Biotechnology
2
Voltage Division
For example, we know
i = VTOTAL / (R1 + R2 + R3)
so the voltage over the first resistor
is
V1=i R1 = R1 VTOTAL / (R1 + R2 + R3)
R1
v1 = V
R1 + R2 + R3
To find the voltage over an individual resistance in series, take the total series
voltage and multiply by the individual resistance over the total resistance.
Dr.-Eng. Hisham El-Sherif
Electronics and Electrical Engineering Department
ELCT708: Electronics for Biotechnology
3
Example
determine the voltage across each resistor
Dr.-Eng. Hisham El-Sherif
Electronics and Electrical Engineering Department
ELCT708: Electronics for Biotechnology
4
Example
determine the voltage across
each resistor
vs
is =
R1 + R2
R1
v1 =
vs
R1 + R2
R2
v2 =
vs
R1 + R2
iS
iS
Dr.-Eng. Hisham El-Sherif
Electronics and Electrical Engineering Department
ELCT708: Electronics for Biotechnology
5
Summary
•The source voltage v is divided among the resistors in direct proportion
to their resistances
•the larger the resistance, the larger the voltage drop.
•This is called the principle of voltage division,
•In general
If a voltage divider has N resistors (R1,R2, . . . , RN) in series with the
source voltage v, the nth resistor (Rn) will have a voltage drop of
Dr.-Eng. Hisham El-Sherif
Electronics and Electrical Engineering Department
ELCT708: Electronics for Biotechnology
6
Current Division
If we know the current flowing into two parallel resistors, we can find out how
the current will divide up in one step.
v
i1 =
R1
1
R1 R 2
i1 =
i
R1 R1 + R2
Dr.-Eng. Hisham El-Sherif
Electronics and Electrical Engineering Department
R2
i1 = i
R1 + R2
ELCT708: Electronics for Biotechnology
7
Note that this differs slightly from the voltage division formula for series resistors
R2 = 0 implies that i1 = 0, i2 = i.
Dr.-Eng. Hisham El-Sherif
Electronics and Electrical Engineering Department
R2 = , that is, R2 is an open
, then
R2
Req = R1
ELCT708: Electronics for Biotechnology
8
Example
Find i1 and i2 in terms of is
is = i1 + i2
is
R1
i1
R2
i2
v1 = v2
i1 R1 = i2 R2
R1
R1
R2 + R1
= i1
i2 = i1
is = i1 + i1
R2
R2
R2
R2
i1 = is
R1 + R2
R1
i2 = is
R1 + R2
Dr.-Eng. Hisham El-Sherif
Electronics and Electrical Engineering Department
ELCT708: Electronics for Biotechnology
9
Example
Use Voltage and current division rules to find Vo and io
6⋅3
=2
6+3
Step 1
Step 1
Step 2
Dr.-Eng. Hisham El-Sherif
Electronics and Electrical Engineering Department
ELCT708: Electronics for Biotechnology
10