=

V

I

**History**

Born on 12 March 1824 – 17 October 1887.

Kirchhoff's Voltage Law

V

Series

=

V

1

V

2

V

3

+

+

V

Series

=

V

1

V

2

V

3

=

=

A series circuit has only one path, so the loads have to share the electric potential.

A parallel circuit has more than one path, so the loads and the source must be the same.

Kirchhoff's Current Law

I

Series

=

I

1

I

2

I

3

=

=

I

Parallel

=

I

1

I

2

I

3

+

+

Junction

A series circuit has only one path, so there can only be one current.

**Introduction**

Electric Current

Electric Current

A parallel circuit has more than one path, so the current can split, depending on the number of paths.

The ohm is a unit of electrical resistance. named after German physicist Georg Simon Ohm.

Direct Current (DC): the movement of electrons in only one direction.

**Ohm**

What is a current? What is the purpose of a current in a circuit?

Ohm's Law

The voltage in a conductor is proportional to the current if the temperature remains constant.

Therefore,

V = constant x I

R

=

V

I

**Δt**

**=**

**Q**

**I**

The Current Equation

R=resistance measured in ohms (Ω), V=electrical potential difference in volts (V), and I=electric current measured in amperes (A).

In any complete path in an electric circuit, the total electric potential increase at the source(s) is equal to the total electric potential decrease throughout the rest of the circuit.

In 1845, German physicist Gustav Kirchhoff came up with 2 laws: one described the electric potential difference and the other the electric current in circuits.

In a closed circuit, the amount of current entering a junction is equal to the amount of current exiting a junction.

**Using the Current Equation**

Ex. Calculate the amount of current through a wire that has 0.85 C of electrons passing a point in 2.5 minutes.

**Δt**

**=**

**Q**

**I**

He discovered that as the amount of voltage increased, the amount of electric current also increased.

**150s**

**=**

**0.85C**

**I**

**=**

**I**

0.0057A

The current is 0.0057 amperes.

**Ex. Calculate the amount of charge travelling through a car battery when a current of 800A is produced for 2 minutes.**

**Q = I x Δt**

**Q = (800A)(120)**

**Q = 96000C**

The amount of charge is 96000 coulombs.

**Electrical Resistance**

So... what is electrical resistance?

Electrical Resistance: a measure of how difficult it is for a current to travel through a material.

**Series and Parallel Circuits**

**A series circuit has only one path, so there can be only one possible current.**

**A parallel circuit has more than one complete path, so the current can split, depending on the number of paths.**

**Resistors**

**Resistor: an electrical device that has a specific resistance value.**

**When would we use resistors?**

**To Calculate Resistance**

**Ohm's Law has to be used**

**I**

**=**

**V**

**R**

**In Series**

**In Parallel**

The resistors are placed one after the other

How to Calculate Voltage and Current in Series and Parallel

V

=

E

Q

I

=

t

Q

Series

V

Series

=

V

1

V

2

V

3

+

+

Parallel

I

Parallel

=

I

1

I

2

I

3

+

+

**I**

**=**

**V**

**R**

**I**

**=**

**V**

**R**

I

Series

=

I

1

I

2

I

3

=

=

V

Parallel

=

V

1

V

2

V

3

=

=

To calculate R , just add the resistances

series

I

R

series

series

=

I

1

R

R

R

2

3

series

+

+

I

series

I

series

R

series

=

1

R

R

R

2

3

+

+

...

...

Examples

You cannot directly add all of the resistances

V

R

parallel

parallel

=

V

1

R

R

R

2

3

parallel

+

+

V

Parallel

V

Parallel

...

R

parallel

=

1

R

R

R

2

3

+

+

...

1

1

1

1

= 10

= 7

= 13

What is the total resistance in the ciruit?

R

series

=

1

R

R

R

2

3

+

+

R = 10 + 7 + 13

series

R = 30

series

Examples

= 75

= 50

= 30

R

parallel

=

1

R

R

R

2

3

+

+

1

1

1

1

R

parallel

=

30

75

50

+

+

1

1

1

1

R

parallel

=

150

150

150

+

+

1

2

3

5

R

parallel

=

150

1

10

R = 15

parallel

**4**

**R = 3.75**

parallel

**R**

series

**=**

3

**R**

**R**

parallel

**+**

**R = 10 + 3.75**

series

**R = 13.75**

series

1

R

R

2

R

3

5

15

10

=

=

=

R

parallel

=

1

R

R

2

+

1

1

1

R

parallel

=

5

15

+

1

1

1

R

parallel

=

15

15

+

1

3

1

R

parallel

=

15

1

4

R = 3.75

parallel

+

R = 10 + 3.75

series

R = 13.75

series

R

series

=

3

R

R

parallel

+

R = 10 + 3.75

series

R = 13.75

series

Total Resistance = 13.75