Ohm’s Law

Objective:

TSW understand the concepts of Voltage, Current, and Resistance by developing and applying Ohm’s Law.

Circuit simulation

R

V

II

I

I

I

I

I

V = Voltage = A potential difference that motivates charge to flow. The pump. (units: V = J/C)

I = current = The amount of charge that flows per unit time. (units: C/s = Amps A)

R = Resistance = A property of the material that resists the flow of current. (units: Ohms Ω = V/A)

Let’s learn how these three quantities are related by imaging different Voltages with a constant Resistance.

Predict the current with a large voltage and a small resistance:

V and R IPredict the current with a small voltage and a large resistance:

RandV I

Let’s come up with an equation for the current (I) that related to the Voltage (V) and Resistance (R):

A large voltage (V) with a small resistance (R) results in a large current (I).

V and R IA small voltage (V) with a large resistance (R) results in a small current (I).

RandV I

I =VR

= IV

R

=IVR

This equation can be rearranged to form Ohm’s Law:

R

VI

IRV

Here are some graphs that represent the relationship:

V

I

R IRV

I

R

R

VI

When we talk about electricity we often refer to the quantity power.

Let’s define power as it relates to an electrical circuit.

The power is large when a large voltage (V) is used to produce a large current flow (I).

IVP

Power is the rate at which energy is used. Units: (J/s =Watt)

Check out the units:

C

J

s

C)(WWatt

s

J

The power equation can be combined with Ohm’s Law to give several variations in order calculate the power.

IVP

RIP

IRIP2

)(

IRV IVP

IR

V

R

VP

VR

VP

2

)(

Example 1: A 60W/120V light bulb is connected to a 120V power supply. What is the resistance of the light bulb and the current flowing in the circuit?

AI

I

IVP

5.0

)120(60

240

)5.0(120

R

R

IRV

The same 60W/120V light bulb is connected to a 240V power supply. What will be different from the calculations above?

Since resistance is a property of the light bulb it will be the same as above, but the current and power of the bulb will be greater.

AI

I

IRV

1

)240(240

WP

P

IVP

240

)240)(1(

Circuit Analysis

Objective: TSW will apply voltage, current and resistance to predict the behavior of various circuits by completing a VIP chart.

Series Circuit

• Current is the same.• Voltage is split.• When one bulb goes out, all go out• Greatest resistance is the brightest.

• Rs=R1+R2+R3+...

is RR

R2

R3

24V

R1

I

Each resister represents a light bulb. Complete the VIP chart in order to rank the brightness of the bulbs.

V I P

Batt

R1

R2

R3

Series CircuitR1=3Ω

R2 =

5Ω

R3=4Ω

24V

Each resister represents a light bulb. Complete the VIP chart in order to rank the brightness of the bulbs.

V I P

Batt

R1

R2

R3

Series CircuitR1=2Ω

R2 =

3Ω

R3=5Ω

12V

Parallel Circuit• Voltage is the same.• Current is split.• When one bulb goes out, others stay the same.• Least resistance is the brightest

• 1/Rp=1/R1+1/R2+1/R3+ …

ip RR

11

R1

R312V

R2 I3

I2I1

I

Each resister represents a light bulb. Complete the VIP chart in order to rank the brightness of the bulbs.

V I P

Batt

R1

R2

R3

Parallel Circuit

R1 =

5Ω

R3 =

10Ω12V

R2 =

2Ω

12V

R1 =

5Ω

R3 =

10Ω

R2=2Ω

Each resister represents a light bulb. Complete the VIP chart in order to rank the brightness of the bulbs.

V I P

Batt

R1

R2

R3

Parallel Circuit

R1 =

3Ω

R3 =

4Ω24V

R2 =

8Ω

Combined Circuits• Map the currents. Currents divide at junctions• Find the total resistance. Start with resistors in series. • Resistors in series have the same current flowing

through them.• Resistors in parallel have the same voltage (potential

difference)• Use Ohm’s law to find the main current.• Use the loop rule to find the voltage (potential difference)

across individual resistors.• Use proportional thinking to find the current flowing

through individual resistors.• Complete the VIP chart. • Check: The power of individual resistors should always

add to the power of the battery.

Each resister represents a light bulb. Complete the VIP chart in order to rank the brightness of the bulbs.

V I P

Batt

R1

R2

R3

Parallel Circuit

R2 =

4Ω

R1=4Ω

R3 =

4Ω12V

Each resister represents a light bulb. Complete the VIP chart in order to rank the brightness of the bulbs.

V I P

Batt

R1

R2

R3

Parallel Circuit

R2 =

2ΩR

1 =4Ω

R3 =

3Ω12V

Each resister represents a light bulb. Complete the VIP chart in order to rank the brightness of the bulbs.

V I P

Batt

R1

R2

R3

Parallel Circuit

R2 =

1ΩR

1 =3Ω

R3 =

8Ω15V

Each resister represents a light bulb. Complete the VIP chart in order to rank the brightness of the bulbs.

V I P

Batt

R1

R2

R3

Parallel Circuit

R2 =

3Ω

R1=2Ω

R3 =

5Ω24V

Each resister represents a light bulb. Complete the VIP chart in order to rank the brightness of the bulbs.

V I P

Batt

R1

R2

R3

R4

Parallel CircuitR1=2Ω

R3 =

1Ω

28V R4 =

2Ω

R2 =

3Ω