Equivalent Resistance

Series and Parallel Circuits

Two Kinds of circuits

Circuit Diagrams

• When drawing pictures of circuits, symbols are used as shorthand instead of pictures of components.

Circuit Diagrams

• Instead of a battery, the symbol is used. (Note: sometimes voltage is called emf or

potential difference)

Circuit Diagrams

• Instead of a resistor, the symbol is used.

Circuit Diagrams

• Resistors and batteries will be labeled with their respective values most of the time.

9V

10 Ω

10 Ω

Practice

• Draw a series circuit with a 5V battery and two resistors (one 3Ω and the other 5Ω)

Practice

• Draw a series circuit with a 5V battery and two resistors (one 3Ω and the other 5Ω)

5V

3 Ω

5 Ω

Practice

• Draw a parallel circuit with a 12V battery and two resistors (one 6Ω and the other 2Ω)

Practice

• Draw a parallel circuit with a 12V battery and two resistors (one 6Ω and the other 2Ω)

12V

6 Ω 2 Ω

Using Ohm’s Law (V=IR)

• Ohm’s Law can be applied to

A) the WHOLE circuitor

B) each RESISTOR separately

Ohm’s Law- WHOLE Circuit

• What is Rtotal for the circuit? What is the current?

5V

3 Ω

5 Ω

Ohm’s Law- WHOLE Circuit

• Rtotal:

• I:

5V

3 Ω

5 Ω

85321 RRRtotal

AV

I

IVIRV

6.08

5

)8(5

Ohm’s Law- EACH Resistor

• What is the voltage in each resistor?

5V

3 Ω

5 Ω

Ohm’s Law- EACH Resistor

• What do we know about the current in each resistor?

5V

3 Ω

5 Ω

Ohm’s Law- EACH Resistor

• What do we know about the current in each resistor?

5V

3 Ω

5 Ω

21 IIItotal

Ohm’s Law- EACH Resistor

• With that in mind we can solve for voltage.3Ω resistor 5Ωresistor

5V

3 Ω

5 Ω

Ohm’s Law- EACH Resistor

• With that in mind we can solve for voltage.3Ω resistor 5Ωresistor

5V

3 Ω

5 Ω

VV

AV

IRV

8.1

)3)(6.0(

Ohm’s Law- EACH Resistor

• With that in mind we can solve for voltage.3Ω resistor 5Ωresistor

5V

3 Ω

5 Ω

VV

AV

IRV

8.1

)3)(6.0(

VV

AV

IRV

0.3

)5)(6.0(

Ohm’s Law- EACH Resistor

• Double check your answer to be sure.3Ω resistor 5Ωresistor

5V

3 Ω

5 Ω

VV

AV

IRV

8.1

)3)(6.0(

VV

AV

IRV

0.3

)5)(6.0(

VV 0.38.1

Summary- SERIES Circuits

• We can write the ways we used Ohm’s Law as:

...

...

...

321

321

321

RRRR

IIII

VVVV

total

total

total

Whole Resistor 1, Resistor 2, Resistor3, …Circuit

Practice

• Pg. 650 Practice A

Ohm’s Law for PARALLEL circuits

PARALLEL (WHOLE circuit)

• First, let’s look at Total Resistance

10V

2 Ω 4 Ω

...1111

321

RRRRtotal

PARALLEL (WHOLE circuit)

10V

2 Ω 4 Ω

...1111

321

RRRRtotal

total

total

total

total

R

R

R

R

33.1

75.0

1

75.01

4

1

2

11

PARALLEL (WHOLE circuit)

• Now we can apply Ohm’s Law (V=IR) to the whole circuit:

V=10V Rtotal=1.33Ω I=?

V=IR → 10V=I(1.33Ω)

I=7.51A10V

2 Ω 4 Ω

PARALLEL (EACH resistor)

• Now lets look at the VOLTAGE in each resistor.

10V

2 Ω 4 Ω

PARALLEL (EACH resistor)

• How much voltage will an electron use up going through this resistor?

10V

2 Ω 4 Ω

PARALLEL (EACH resistor)

• How about this one?

10V

2 Ω 4 Ω

PARALLEL (EACH resistor)

• Since the VOLTAGE is the same in each resistor

10V

2 Ω 4 Ω

...321 VVVVtotal

PARALLEL (EACH resistor)

• Now use V=IR to solve for current at each resistor:

2Ω resistor 4Ω resistor

10V

2 Ω 4 ΩV= 10V V= 10V

IA

IV

IRV

5

)2(10

IA

IV

IRV

5.2

)4(10

PARALLEL (EACH resistor)

Total Circuit: V=10V Rtotal=1.33Ω I=7.51A

Compare the currents2Ω resistor 4Ω resistor

10V

2 Ω 4 ΩV= 10V V= 10V

IA

IV

IRV

5

)2(10

IA

IV

IRV

5.2

)4(10

Equal

+

Summary of Ohm’s Law

• For PARALLEL circuits:

• Vtotal=V1=V2=V3=…

• Itotal=I1+I2+I3+…

• ...1111

321

RRRRtotal

10V

2 Ω 4 Ω

Practice

• Pg. 655 Practice B