Download Insert Fig. 7.22

Series Current
Since there is only one path for the current,
the current in a series circuit is the same
everywhere.
Series Voltage Drops
In a series circuit the sum of the voltage
drops across each resistor or device is equal
to the potential difference applied across the
combination (i.e. the battery voltage).
VBattery  VR1  VR 2  VR 3  VR 4  VR 5  ...
Series Resistance
The total resistance of resistors in series is the
sum of the individual resistances.
RTotal  R1  R2  R3  R4  R5  ...
Series Resistance
Parallel Current
In a parallel circuit the total current through
the battery is equal to the sum of the current
through the branches.
IBattery  I1  I2  I3  I4  I5  ...
Parallel Resistance
The inverse of the total resistance of resistors
in parallel is the sum of the inverses of the
individual resistances.
1
RTotal
1
1
1
1
1
 



 ...
R1 R2 R3 R4 R5
Parallel Resistance
Equivalent Resistance
1
1
1
1



18 9 6 Req
1
2
3


18 18 18
6
1
1



18 3 Req
3Ω + 12Ω = 15Ω
What is the current I ?
V=IR; I = V/R = 30V/15Ω = 2 A
Equivalent Resistance
1
1
1


1  3 7  5 Req
3
1
1
4



12 12 Req 12
What is the current I ?
V=IR; I = V/R = 48V/3Ω = 16 A
Descriptive Examples
Example – Calculate the indicated currents (Is , I5)
and voltage (V7) in the circuit below.
Insert Fig. 7.22
Descriptive Examples
Example – Calculate the indicated currents (Is , I5)
and voltage (V7) in the circuit below.
Insert Fig. 7.22
Left 1. Collapse series R1 , R2 , R3 into R1+2+3.
Descriptive Examples
Example – Calculate the indicated currents (Is , I5)
and voltage (V7) in the circuit below.
Insert Fig. 7.22
Left 2. Collapse parallel R4 with R1+2+3 into R1+2+3+4.
Descriptive Examples
Example – Calculate the indicated currents (Is , I5)
and voltage (V7) in the circuit below.
Insert Fig. 7.22
Left 3. Combine series R5 with R1+2+3+4 into R1+2+3+4+5.
Descriptive Examples
Example – Calculate the indicated currents (Is , I5)
and voltage (V7) in the circuit below.
Insert Fig. 7.22
Left 4. I5 = 72 V/R1+2+3+4+5
Descriptive Examples
Example – Calculate the indicated currents (Is , I5)
and voltage (V7) in the circuit below.
Insert Fig. 7.22
Right 1. Collapse series R8 , R9 into R8+9.
Descriptive Examples
Example – Calculate the indicated currents (Is , I5)
and voltage (V7) in the circuit below.
Insert Fig. 7.22
Right 2. Collapse parallel R7 and R8+9 into R7+8+9.
Descriptive Examples
Example – Calculate the indicated currents (Is , I5)
and voltage (V7) in the circuit below.
Insert Fig. 7.22
Right 3. Collapse series R7+8+9 and R6 into R6+7+8+9.
Descriptive Examples
Example – Calculate the indicated currents (Is , I5)
and voltage (V7) in the circuit below.
Insert Fig. 7.22
Right 4. I6 = 72 V/R6+7+8+9
Descriptive Examples
Example – Calculate the indicated currents (Is , I5)
and voltage (V7) in the circuit below.
Insert Fig. 7.22
Right 5. Is = I5 + I6
Descriptive Examples
Example – Calculate the indicated currents (Is , I5)
and voltage (V7) in the circuit below.
Insert Fig. 7.22
Right 6. V7 = 1/2 I6 X R7