13.3 emf and internal resistance

What is electromotive force (emf)?

Electrical energy per unit charge produced by a source

What is the unit of emf?

Volt (V)

What is internal resistance?

Resistance inside a cell that opposes the flow of charge

Why is terminal pd less than emf?

Energy is lost as heat due to internal resistance

What is the formula relating emf and internal resistance?

𝜀

=

𝐼

𝑅

+

𝐼

𝑟

ε=IR+Ir

What does

𝜀

=

𝐼

𝑅

+

𝐼

𝑟

ε=IR+Ir represent?

Emf equals terminal pd plus lost pd

How is current related to emf and total resistance?

𝐼

=

𝜀

/

(

𝑅

+

𝑟

)

I=ε/(R+r)

What is lost pd?

Pd across internal resistance equal to

𝐼

𝑟

Ir

What is the power supplied by the cell?

𝑃

=

𝐼

2

𝑅

+

𝐼

2

𝑟

P=I

2

R+I

2

r

When is maximum power delivered to a load?

When load resistance equals internal resistance,

𝑅

=

𝑟

R=r

How can terminal pd be measured?

Using a high-resistance voltmeter across cell terminals

Why does terminal pd decrease with increasing current?

More current increases lost pd across internal resistance

What is the gradient of a

𝑉

V-

𝐼

I graph?

Negative gradient equal to

−

𝑟

−r

What is the y-intercept of a

𝑉

V-

𝐼

I graph?

The emf of the cell

How is internal resistance calculated from two current-pd pairs?

𝑟

=

(

𝑉

1

−

𝑉

2

)

/

(

𝐼

2

−

𝐼

1

)

r=(V

1

​

−V

2

​

)/(I

2

​

−I

1

​

)

What happens to terminal pd at zero current?

Terminal pd equals emf since no energy is lost

How is internal resistance shown in a circuit?

As a resistor in series with the cell

Advanced Questions:

Why is matching load resistance important?

Maximizes power transfer by ensuring

𝑅

=

𝑟

R=r

What factors affect internal resistance?

Material properties, temperature, and age of the cell

How does increasing current affect efficiency?

Efficiency decreases as lost pd increases with higher current

What is the physical origin of internal resistance?

Opposition due to ion movement and material resistivity within the cell

Why is emf constant but terminal pd variable?

Emf depends on chemical energy, while terminal pd depends on current

How is power wasted in a cell?

𝑃

wasted

=

𝐼

2

𝑟

P

wasted

​

=I

2

r, energy dissipated as heat in internal resistance

Exam Questions:

Explain why terminal pd decreases as current increases.

Higher current causes greater lost pd across internal resistance

A cell has emf

6.0

V

6.0V and internal resistance

0.5

Ω

0.5Ω. Calculate the terminal pd with

2.0

A

2.0A.

𝑉

=

𝜀

−

𝐼

𝑟

=

6.0

−

(

2.0

×

0.5

)

=

5.0

V

V=ε−Ir=6.0−(2.0×0.5)=5.0V

Why does a graph of

𝑉

V vs.

𝐼

I have a negative gradient?

The internal resistance

𝑟

r reduces terminal pd as current increases

Describe the relationship between emf and internal resistance using an experiment.

Measure

𝑉

V and

𝐼

I for different loads, plot

𝑉

V-

𝐼

I, find gradient as

−

𝑟

−r and y-intercept as

𝜀

ε

A cell's terminal pd is

1.2

V

1.2V at

0.3

A

0.3A and

1.5

V

1.5V at

0.1

A

0.1A. Find

𝑟

r and

𝜀

ε.

𝑟

=

(

1.5

−

1.2

)

/

(

0.1

−

0.3

)

=

1.5

Ω

r=(1.5−1.2)/(0.1−0.3)=1.5Ω,

𝜀

=

1.5

+

(

0.1

×

1.5

)

=

1.65

V

ε=1.5+(0.1×1.5)=1.65V

What is the condition for maximum power transfer in a circuit?

Load resistance equals internal resistance,

𝑅

=

𝑟

R=r

Why does terminal pd equal emf when no current flows?

No energy is lost in internal resistance at zero current