D.C. Circuits | E.M.F. & Internal Resistance

D.C. Circuits

E.M.F. & Internal Resistance

CIE 9702 AS Level Physics

SMALHB Physics 2021/2022

Prepared by: Tcr. Nadheerah

​"In the name of Allah, the Most Gracious, the Most Merciful"

RECALL...

Let's attempt the questions in the following slides

Multiple Choice

Electromotive Force (e.m.f.) is defined as...

• energy passing through a power source

• energy needed to power up a circuit per unit charge

• energy converted to electrical energy per unit charge

• energy converted from electrical to other forms per unit charge

Multiple Choice

Potential difference is the energy converted from electrical energy to other forms per unit charge.

• CORRECT

• WRONG

Electromotive force (e.m.f.)

• ​energy converted from other forms of energy to electrical energy

• ​per unit charge

Potential difference (p.d.)

• ​energy converted from electrical energy to other forms

• ​per unit charge

​often 2 marks each!

Internal Resistance

The figure shows a circuit set to the following values:

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• ​e.m.f. of cell:        9.0 V

• ​resistor:              10.0 Ω

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​Notice that the current flowing through the circuit is 0.82 A.

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​BUT V = IR:

​I = 0.90 A

​Where does the 0.08 A current flow?

Internal Resistance

The p.d. across the cell is then measured.

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p.d. of cell = 8.18 V

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​The cell was set to have an e.m.f. of 9.0 V, but only have a p.d. of 8.18 V!

In reality:

the voltage measured across the cell is known as the terminal p.d.

​some of the e.m.f. are lost within the cell​

Internal Resistance

The cell is said to have an internal resistance

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​The amount of electrical energy lost within the cell is known as lost volts

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​The electrical energy used to 'power up' the circuit is the terminal p.d.

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​Meanwhile, the total electrical energy in the circuit remains equal to the e.m.f.

Before moving on to the next slide, can you think of an expression which relates the e.m.f., terminal p.d. and the lost volts?

Open Ended

Suggest an equation which shows the relationship between the e.m.f. (E), terminal p.d. (V_R) and lost volts (V_r).

Internal Resistance

Can you try and express the above equation in terms of:

• ​current, I

• ​resistance of resistor, R

• ​internal resistance of cell, r

​E.M.F. = TERMINAL P.D. + LOST VOLTS

​

​E = V_R + V_r

Well done and thank you for your attempts!

Open Ended

Using V = IR, suggest an expression relating the e.m.f (E), current in the circuit (I), resistance of the resistor (R) and the internal resistance of the cell (r).

Internal Resistance

In reality:

​We cannot measure the e.m.f. of the cell directly.

​Can you think of plotting the above values in a graph? What value is the e.m.f.?

​E = IR + Ir

​E = I(R + r)

Well done and thank you for your attempts!

Multiple Choice

A student wants to investigate the value of the e.m.f. of a cell.

A graph of terminal p.d. against current is plotted.

Which of the following are true?

• E = y-intercept

• E = gradient

• E = gradient/current

• E = Ir + IR

Internal Resistance

Well done and thank you for your attempts!

​​E = I(R + r)

​We can measure the current flowing through the circuit as we change the load resistor, R.

​

​Theoretically, if the cell does not have any internal resistance, the y-intercept is equal to the e.m.f., i.e. the maximum amount of voltage the cell supplies

Internal Resistance

Well done and thank you for your attempts!

​​E = I(R + r)

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​The gradient of the graph is equal to -r.

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​Hence, we can also investigate the internal resistance of the cell.

Power and Internal Resistance

The following circuit enables us to measure the power delivered by the cell using P=IV

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​It is found that, as we change the load resistor values, the power has a maximum when the load resistance is equal to the internal resistance!

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​Internal Resistance

​Summary:

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• ​E.M.F = energy to electrical / charge

• ​P.D. = electrical to other energy / charge

• ​​​E = V_R + V_r = I(R + r)

• ​extrapolate V-I graph for E

• ​maximum cell power when R = r

​More resources:

• ​https://www.youtube.com/watch?v=9r3Xgd79MFw

• ​https://www.youtube.com/watch?v=3OEJ6eok-Zs