Lesson 5 — 5,3 Series and paralel

• Physics
• Middelbare school
• vwo
• Leerjaar 3

This lesson

• Quick recap
• Discussing the homework
• Different types of Resistors
• Start 5,3

Quick recap

Current, voltage, Resistance

Water tank comparison.

Current, voltage, Resistance

Ohm's law

R=​I​​U​​

I=​R​​U​​

Specific resistivity

R=​A​​ρ⋅l​​

Every material has a specific measure of how much it resists the flow of current. 

This property is called the

Specific resistivity of a material.

The formula on the right shows what the resistance of a piece of wire becomes.

• R: Resistance  — Ohm (Ω)
  
• ρ: the resistivity — Ohm-meter (Ωm)
• l: the length of the wire — meters (m)
• A: the area of the cross section of the wire — (m²)

Discussing the homework

Worksheet:

< Part 2 Exercise 1 to 4 + 6 & 7

> Part 2 Exercise 1, 2, 5, 8 & 9

Worksheet part 1

Water tank comparison	Unit in terms of water	Property of an electric circuit	Unit	Base units behind this unit
The height difference between the valve and the top of the water.	Joule/ Litre	Voltage	Volt (v)	Joule/ Coulomb
The flow of water.	Litre/ second	Current	Ampere (A)	Coulomb / second
How open or closed the valve is.	Not required	Resistance	Ohm (Ω)	Not required

1) Think about the water tank comparison.

a) The water flow of water will increase / decrease when the valve gets opened more.

b) The electric current in a circuit will increase / decrease when the resistance increases.

c) The flow of water will increase / decrease when the height difference between the valve and the top of the water tank increases.

d) The electric current in a circuit will increase / decrease when the voltage over the circuit increases.

2) Which of the circuits below is correct for measuring voltage and current? 

 A physicist wants to make a charge of 6,4∙10^-15 C flow through a wire. He knows the resistance of the wire is 25 Ω. He applies a voltage of 8 V over the wire. How long does a current have to flow through the wire to let the required amount of charge flow through it?

Given:

- Required amount of charge: 6,4 • 10^15

- R = 25 Ω

- U = 8 V

Asked:

How long does current have to flow through the write to reach the required amount of charge?

Working:

R = U/I                   I = U/R

Q = I • t                  t = Q/ I

I = 8/ 25 = 0.32 A

t = (6,4 • 10^15)/ 0,32 = 2 • 10^16 seconds

 A wire has a cross-section with an area with a radius of 3 cm. The length of this wire is 20 cm. The resistance of this wire is 1,56∙10^(-6) Ω. The temperature of the wire is 20 ºC. What material is it made of? Use the table one 1 on page 79 of Book B to find the answer.

Given:

- r cross section wire = 3 cm = 0,03 m

- A cross section wire = π • r2 = π  • 0,032 = 0.00282743338 m2

- l wire = 20 cm = 0,2 m.

- R = 1,56 x 10-6 Ω

Asked:

What material is the wire made off? 

Working:

R = (ρ • l) / A                  ρ = (R • A) / l

ρ = ( (1,56 x 10-6) • 0.00282743338) / 0,2 = 0,022 • 10-6 Ωm

This corresponds with the specific resistivity of gold. So the wire must be made of gold.

Different types of resistors

• What is an ohmic resistor?
  
•  What material can be used to make an ohmic resistor?
• Why do other materials not follow Ohms law?
• What does NTC stand for?
• What is the relationship between temperature and resistance in an NTC?
• What would the opposite of an NTC be called?
• What doe LDR stand for?
• What is the relationship between light and resistance in an LDR?

Different types of resistors

What is an ohmic resistor?

• A resistor where the resistance is the same regardless of the voltage.

 What material can be used to make an ohmic resistor?

• Constantan

Why do other materials not follow Ohms law?

• An increase in voltage causes an increase in current in a circuit. This increases the temperature of the wire. This causes the resistance to increase.

Different types of resistors

What does NTC stand for?

• Negative temperature coefficient. 

What is the relationship between temperature and resistance in an NTC?

• An increase in temperature causes a decrease in resistance and vice versa.

What would the opposite of an NTC be called?

• A PTC — Positive Temperature Coefficient.

What doe LDR stand for?

• Light dependent resistor.

What is the relationship between light and resistance in an LDR?

• If more light falls on the reistor its resistance will decrease and vice versa.

Resistance, voltage & current — Series circuit

Resistors in series

Voltage in series

Current in series

R​tot​​=R​1​​+R​2​​+R​3​​+...

U​tot​​=U1+U2+U3...

I​tot​​=I​1​​=I​2​​=I​3​​=...

Resistance, voltage & current — Parallel circuit

Resistors in series

Voltage in series

Current in series

​R​​1​​​tot​​=​R​​1​​​1​​+​R​​1​​​2​​+​R​​1​​​3​​+...

I​tot​​=I​1​​+I​2​​+I​3​​=...

U​tot​​=U​1​​=U​2​​=U​3​​=...

Homework next lesson

5,3 Exercise 1, 2, 3 & 4