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1

Chapter Two

Potential Difference

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2

Objective

Define Potential Difference

Sign and Unit

Measurement of Potential difference

Laws of Potential Difference

Coulomb’s Law

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Define Electric potential Difference

What does “1.5 Volts” indicated on the battery mean?

What does the electric potential difference between the ends is 1.5 Volts?

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4

1.5 V

230 V

100,000 V

So what is a volt?

Define Electric potential Difference

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Define Electric potential difference

The electric potential difference [∆V] in Volts between two points: is the work in Joules needed to move 1C of charge between those points.

∆V is measured in Volts[V]: 1V =1J/C.

The 1.5 V battery does 1.5 J of work for every 1 C of charge flowing round the circuit

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Sign and Unit

• We can say the potential difference is an algebraic quantity.

• The potential difference between two points A and B can be positive or negative depending on whether V_A > V_B or V_A < V_B .

V_BA = V_B - V_A

V_BA = -V_AB

V_AB = V_A - V_B

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Sign and Unit

• The potential difference is measured in Volts (V).
• Example: The potential difference of the given battery is V=1.5Volts .

The SI Unit is Volt (V)

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Measurement of Potential Difference

The potential difference is measured by using:

Note: to measure the voltage we connect the instrument in parallel with the load.

1. Digital Voltmeter.

2. Analog Voltmeter.

3. Oscilloscope.

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Measurement of Potential Difference

The potential difference is measured by using:

1. The Digital Voltmeter.

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Measurement of Potential Difference

The potential difference is measured by using:

1. The analog Voltmeter.

To measure a certain voltage VAB:

• Connect A to terminal V and B to COM terminal (V_AB = U_V-COM).
• The voltmeter must set to a scale (range) just greater than the measured voltage.

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Measurement of Potential Difference

How to calculate voltage (V_AB = U_V-COM )?

Where:

d: number of divisions corresponding to the deviation of the needle

D: total number of deviations

S: scale or chosen range

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Measurement of Potential Difference

Example 1:

We have an analog voltmeter having the ranges: [1V; 3V; 5V; 10V; 15V; 30V ] and composed of 150 divisions.

1. Draw a figure showing the branching of the volt meter across a battery of U_PN = 12V.
2. Calculate the deviation of the needle after choosing the most convenient scale (range).

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Measurement of Potential Difference

 solution of Example 1:

1. See the figure.

2. Given U_PN = 12V and D =150div; then the convenient scale (range) is: S= 15V.

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14

Measurement of Potential Difference

The potential difference is measured by using:

3. Oscilloscope.

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Laws of Potential Difference

1. Law of addition of potential difference:

Given the following circuit containing loads connected in series with the battery.

V = V1 + V2 +V3 +…

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Laws of Potential Difference

2. Law of uniqueness of potential difference:

The P.D between the terminals of loads connected in parallel are equal.

V = V1 = V2 =V3 =…

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Grade 10 Solving problems 2019 – 2020

Given five identical lamps connected to a DC generator as shown. A digital voltmeter that indicates V = -12V.

1. Indicate the voltage measured by the voltmeter then deduce the voltage across the terminals of the generator.

Exercise 1: Measuring of Potential Difference

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Grade 10 Solving problems 2019 – 2020

Now an oscilloscope are connected across the terminals of the generator.

2. We observe on the screen a luminous line displaced by 4 divisions.
1. Indicate with justification whether this line is displaced upward or downward.
2. What would we observe in the absence of sweeping?
3. Determine the vertical sensitivity adjusted.
3. Calculate the potential difference across each lamp.

Exercise 1: Measuring of Potential Difference

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19

Grade 10 Solving problems 2019 – 2020

Solution of exercise 1:

• The measured voltage is V_NP= -12V.

V_G = V_PN =-VNP = -(-12V) → V_G =12V.

3. .
1. The luminous line displaced 4 div upward, because the channel of the oscilloscope is connected to (+) pole of generator while the ground is connected to (–) pole.
2. We observe a luminous spot moves 4 div upward from the central axis of the oscilloscope.

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20

Grade 10 Solving problems 2019 – 2020

Solution of exercise 1:

2. .
3. V_G = S_V × y → 12V = S_V × 4div → S_V = 12/4 = 3V/div.
3. V_PN = V_PA + V_AB + V_BC + V_CD + V_DN

All the lamps are identical; then V_AB = V_BC = V_CD

12 = 0 + 3V_AB + 0; then V_AB = 12/3 = 4V.

V_AB = V_BC = V_CD = 4V

V_PN = V_PA + V_AE + V_ED + V_DN ; V_AE = V_ED (identical lamps)

12= 0 + V_ED +V_ED + 0; then 2V_ED = 12V → V_ED =6V

V_ED = V_DN = 6V

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Grade 10 Solving Problems 2019 – 2020

Six electric loads are connected to a 24V battery as shown in the adjacent figure. Given: U_PA = 8V; U_ND = -4V; and U_AC = 6V.

Exercise 2:

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Grade 10 Solving Problems 2019 – 2020

1. Calculate the electric potential differences: V_DN, V_AD, and V_CD.
2. C is taken as a reference potential. Determine the electric potentials V_C, V_A, and V_P.

Exercise 2:

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Grade 10 Solving problems 2019 – 2020

Solution of Exercise Two

1. V_DN = -V_ND → V_DN = 8V.

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V_PN = V_PA +V_AD + V_DN → V_AD = V_PN - V_PA - V_DN

→V_AD = 24V – 8V – 4V → V_AD = 12V

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V_AD = V_AC +V_CD →V_CD = V_AD – V_AC → V_CD = 12V – 6V

→V_CD = 6V.

2. V_C = 0

V_AC = V_A – V_C → V_A = V_AC + V_C → V_A = 6V – 0 → V_A = 6V.

V_PA = V_P – V_A → V_P = V_PA +V_A → V_P = 8V + 6V

→ V_P = 14V.

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Grade 10 Solving problems 2019 – 2020

Exercise 2:

3. An oscilloscope is connected across the two terminals B and C; we observe on the screen of it a luminous line which is displaced upward by 3 div. Given: S_V = 1V/div.
1. Show in a figure the connection of the oscilloscope.
2. Calculate V_BC then deduce V_AB.

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Grade 10 Solving problems 2019 – 2020

Solution of exercise 2:

3. The following:
1. See the figure.

2. V_BC = S_V × y = 1V/div × 3div → V_BC = 3V

V_AC = V_AB + V_BC → V_AB = V_AC – V_BC → V_AB = 6V – 3V

→ V_AB = 3V.

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Grade 10 Solving problems 2019 – 2020

Exercise 3:

Consider the electric circuit represented by figure 1.

The oscilloscope is used to visualize the voltage of the resistor and figure 2 is obtained. Given S_V = 3v/div.

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Grade 10 Solving problems 2019 – 2020

Exercise 3:

1. Redraw figure 1, showing the connection of the oscilloscope across the resistor (R).
2. What voltage does the oscilloscope read V_{BC or} V_CB? Justify.
3. Calculate the voltage measured by the oscilloscope.
4. The used multi-meter, is considered as connecting wire.
1. Show that V_P = V_A.
2. Calculate the potential difference U_AB.

Given : U_PN = 10V.

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Grade 10 Solving problems 2019 – 2020

1. See the figure.

2. The oscilloscope reads V_CB<0 because the screen shows the line deviated downward by 2 divisions.

Solution of Exercise 3:

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Grade 10 Solving problems 2019 – 2020

3. V_CB = S_V × y; V_CB =3V/div × (-2) → V_CB = -6V.�
4. .
1. V_PA = V_P – V_A then:

0= V_P – V_A → V_P = V_A

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2. V_PN = V_PA +V_AB +V_BC + V_CN

10V = 0V + V_AB +6V +0

V_AB = 10V – 6V → V_AB = 4V.

Solution of Exercise 3:

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30

Grade 10 Quiz Time: 30minutes

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Measuring the Electric Potential Difference

During a lab session, group of students wanted to measure the voltage of some electrical components. To do so, they used an analog voltmeter and an oscilloscope. The electric circuit is represented in the adjacent circuit.

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Grade 10 Quiz Time: 30minutes

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Part A: Use analog voltmeter: (1.5 points)

1. Redraw the Circuit showing the connection of the analog voltmeter to measure U_PN. (0.5 point).
2. The used voltmeter to measure UPN has the ranges "1000v, 250v, 50v, 20v, 10v and 5v".

Show that UPN = 6.4V. (1point).

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Grade 10 Solution of Quiz Time: 30minutes

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Part A: Using an analog voltmeter

1. See the figure (0.5 point).

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Grade 10 Quiz Time: 30minutes

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Part B: Using the oscilloscope ( 3.5 points)

1. Calculate the voltage U_FE. Deduce the value of U_EF.

A student connects to the circuit an oscilloscope that permits to measure the voltage U_FE. The following figure is obtained.

Given: S_V = 1V/div.

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Grade 10 Quiz Time: 30minutes

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Part B: Using the oscilloscope ( 3.5 points)

2. A student regulates the vertical sensitivity such that the straight line displaces down one more division. Calculate the new vertical sensitivity.
3. What would you observe on the screen of the oscilloscope if its connections are interchanged.

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Grade 10 Quiz Time: 30minutes

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Solution of Part B: ( 3.5 points)

1. UFE = SV × y → UFE = 1v/div × (-2div) → UFE = -2V.

Then UEF = - UFE = -(- 2V) →UEF = 2V.

2. UFE =S’V × y → S’V = UFE/y = (-2V)/(3) → S’V = 0.67v/div.
3. We observe a St. Line displaces upward by 2 divisions (y = 2 div).

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Grade 10 Quiz Time: 30minutes

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Part C: Circuit analysis (points)

1. Calculate the voltage U_PD.
2. Knowing that the lamps L₁ and L₂ are identical, determine U_AB and U_BC.
3. Show that V_C = V_D= V_E.
4. The point B is grounded. Find V_C and V_P.

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Grade 10 Solution of Quiz Time: 30minutes

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Part C: Circuit analysis:

1. U_DN = U_DP+ U_PN then U_PD = 4.4v.
2. U_EF = U_CB+U_BA, but U_EF= U_EF (parallel connection) then U_CB=U_BA= 1v.
3. U_CD = 0 then V_C =V_D, U_DE = 0v then V_D=V_E therefore V_D=V_E= V_c.
4. V_B = 0v, V_CB = V_C-V_B then V_C=1v. V_p = 5.4v

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End of Chapter Two