Work and Energy: Moving a charge in an electric field involves

doing work, changing its potential energy.

1. Electrical Potential Energy (PE)
Energy a charge possesses due to its position in an electric field.
It is analogous to gravitational potential energy but results from
electric interactions, not gravitational.
Properties
• Depends on:
1. The charge (q).
2. The electric field strength (E).
3. The displacement (d) in the direction of the field.
Equation in a Uniform Electric Field
𝑃𝐸𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐=−𝑞𝐸𝑑
The negative sign indicates that:
A positive charge loses potential energy moving with the field.
A negative charge gains potential energy moving with the field.
Relation to Mechanical Energy
Part of the total mechanical energy:
𝑀𝐸=𝐾𝐸+𝑃𝐸𝑔𝑟𝑎𝑣+𝑃𝐸𝑒𝑙𝑎𝑠𝑡𝑖𝑐+𝑃𝐸𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐
ME=KE+PE grav +PEelastic +PEelectric
2. Electric Potential (V)
Electric potential is the electric potential energy per unit charge at
a point in space:
𝑉=𝑃𝐸𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐/𝑞
Scalar quantity.
Independent of the test charge placed at that location.
Units: Volts (V), where 1 V = 1 J/C.
3. Potential Difference (ΔV)
The change in electric potential between two points:
Δ𝑉=Δ𝑃𝐸𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐/𝑞
This tells us how much energy per unit charge is gained or lost.
In a Uniform Electric Field:
Δ𝑉=−𝐸𝑑ΔV=−Ed
Perpendicular movement to the field results in no change in
potential energy.
4. Electric Potential due to a Point Charge
Equation for Electric Potential at a Distance r
𝑉=𝑘𝐶⋅𝑞1𝑟
Where:
𝑉: electric potential.
𝑘𝐶 : Coulomb's constant (8.99×109𝑁⋅𝑚2/𝐶2
q1 : source charge.
𝑟: distance from the source charge.
Potential Difference Between Two Points
Δ𝑉=𝑘𝐶𝑞1(1/𝑟2−1/𝑟1)
5. Superposition Principle
When multiple charges are present, the total electric potential at a
point is the sum of the potentials due to each charge:
𝑉𝑡𝑜𝑡𝑎𝑙=𝑉1+𝑉2+𝑉3+...
6. Battery and Energy Conversion
Battery Function
Maintains a constant potential difference between its terminals
(e.g., 1.5 V).
Inside the battery:
A chemical reaction does work on charges, moving them from
positive to negative terminal, increasing their electrical potential
energy.
Outside the battery:
Charges move from negative to positive terminal, releasing
energy to the circuit/device.
Energy Transfer
1 C of charge moving across 1.5 V releases 1.5 J of energy.
Once a charge returns to the positive terminal, its potential energy
= 0, ready to be recharged again.
Practical Examples & Problems
Sample Problem A :
A charged oil droplet gains 1.9 × 10⁻¹⁹ J of electrical potential
energy while moving 3.0 cm in a uniform electric field of 2.0 × 10⁴
N/C.
What is the charge on the droplet?
Step 1: List Given Data
Change in potential energy:
Δ𝑃𝐸𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐=1.9×10−19 J
Distance moved:𝑑=3.0 cm=3.0×10−2 m
Electric field strength:𝐸=2.0×104 N/C
E=2.0×10 4 N/C
Unknown:𝑞=?
Step 2: Use the Formula
Δ𝑃𝐸𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐=−𝑞𝐸𝑑
Rearrange to solve for 𝑞
q=−Δ𝑃𝐸𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐/𝐸𝑑
Step 3: Substitute the Values
𝑞=−1.9×10−19 J / (2.0×104 N/C)(3.0×10−2 m)
𝑞=−3.17×10−22 C
(The negative sign indicates the charge is negative, like an
electron.)
Now, Your Turn! Practice Problem
Problem:
A small particle gains 4.0 × 10⁻¹⁸ J of electrical potential energy
while moving 5.0 cm in a uniform electric field of 8.0 × 10³ N/C.
What is the charge on the particle?
Definition and Importance of Capacitance
• A capacitor is an electrical device that stores electric potential energy
through the separation of electric charges.
• Used in many devices: radio tuning circuits, flash in cameras, ignition
systems, and keyboards.
• The charge (Q) on a capacitor is the magnitude of charge on either of its
two plates.
• A charged capacitor can later release energy when needed.

Capacitance Formula
• Capacitance (C) is defined as the ratio of the charge (Q) on each plate to
the potential difference (∆V) across the plates:
C=Q/ΔV
• SI unit: Farad (F) = 1 coulomb/volt (C/V)
• Practical capacitors typically use units like:
o Microfarads (μF = 10⁻⁶ F)
o Picofarads (pF = 10⁻¹² F)

Factors Affecting Capacitance

➤ a. Parallel-Plate Capacitor

• Formula for capacitance in a vacuum:

C=ε0A/d
where:
o ε0 = permittivity of vacuum (8.85×10−12 C2/N⋅m2)
 o A = plate area
o d = separation between plates

Dielectrics and Their Role

• A dielectric is an insulating material (air, rubber, paper, etc.) inserted
between capacitor plates.
• It increases the capacitance by:
o Reducing the effective electric field
o Allowing more charge to be stored at the same potential difference.
• Example: Flashlight or camera flash uses capacitors with dielectrics for rapid
discharge.

Charging and Discharging Capacitors

• Charging: Connecting a capacitor to a battery removes electrons from one
plate and deposits them on the other, until ΔV (potential difference) across
plates = battery voltage.
• Discharging: Connecting the plates with a conductor allows charges to
return, releasing stored energy.

Energy Stored in Capacitors

• Energy is stored as electrical potential energy:

Applications
• Camera flash: Capacitor stores energy then releases it in a quick burst.
• Computer keyboards: Each key alters the capacitance between plates.
 • Sensors: Capacitors are used in touch screens and pressure sensors due to
sensitivity to spacing and materials.

Safety and Limitations

• Capacitors have maximum voltage ratings.
• Electrical breakdown can occur if voltage exceeds the threshold—similar to
lightning in the atmosphere.
Electrical Circuits, Resistance, and Power
1. Electric Current
Electric current is the flow of electric charge through a conductor. It is defined as:
I = Q/ t
ΔQ is the charge (in coulombs, C)
Δt is time (in seconds, s)
1 ampere = 1 coulomb/second
Conventional Current Direction: From the positive terminal to the negative
terminal of a battery.
2. Voltage and Resistance
Voltage (V) is the potential difference across two points in a circuit.
Resistance (R) opposes the flow of electric current and is measured in ohms (Ω).
Ohm’s Law
V = IR
3. Resistivity and Conducting Materials
Resistivity (ρ) is a property of the material and affects resistance:
R = ρ L/A

A is the cross-sectional area

ρ is the resistivity (depends on material and temperature)
Materials with low resistivity (like copper) are good conductors.
4. Electric Power and Energy
Power (P):
P = IV
P = I2R
P = V2/ R
Electrical Energy (E):
E = Pt
If P is in kilowatts (kW) and t in hours (h), E is in kilowatt-hours (kWh).
5. Real-World Applications
Hybrid Cars: Use both chemical and electrical energy; energy loss through
resistive heating.
Electric Heaters: Use high-resistance wires to convert electric energy into heat.
Geothermal Plants: Generate electric power distributed via electric circuits.
Utility Billing: Electricity usage is billed by energy consumed (kWh), not just
power.
6. Sample Problems
Power Output Problem:
A geothermal generator output 1.4 × 10⁸ W. How much energy is produced in 1
hour?
E = P t = (1.4 x108 x 3600= 5.04 x1011 j
Ohm’s Law
A toaster has a resistance of 20 Ω and is connected to a 120 V outlet.
a) What is the current through the toaster?
b) How much power does it consume?
Solution:
I =V/R= 120/20 = 6 A
P = IV = 6x 120 = 720 W
Work and Energy in Electric Fields
1. What does moving a charge in an electric field involve?
A. Producing light
B. Doing work
C. Creating gravity
D. Changing magnetic fields
Answer: B
2. Electrical potential energy depends on all the following EXCEPT:
A. The charge (q)
B. The electric field strength (E)
C. The speed of the charge
D. The displacement (d)
Answer: C
3. What is the unit of electric potential?
A. Newton
B. Joule
C. Volt
D. Coulomb
Answer: C
4. In a uniform electric field, the formula for electric potential energy is:
A. PE = qd
B. PE = -qEd
C. PE = kq/r
D. PE = Vq
Answer: B
5. Electric potential is defined as:
A. Potential energy multiplied by charge
B. Charge divided by energy
C. Potential energy per unit charge
D. Work per unit mass
Answer: C
6. What is the formula for electric potential due to a point charge?
A. V = qEd
B. V = kq/r
C. V = IR
D. V = PE/q
Answer: B

7. what does ΔV represent?

A. Potential energy difference
B. Voltage across resistor
C. Change in electric potential
D. Current
Answer: C
8. What principle allows the addition of electric potentials from multiple point
charges?
A. Coulomb’s law
B. Superposition
C. Kirchoff’s law
D. Gauss’s law
Answer: B

Battery and Energy Conversion

1. What is the role of a battery in a circuit?
A. To increase resistance
B. To maintain potential difference
C. To generate magnetic fields
D. To stop current
Answer: B
2. Inside a battery, what moves the charge?
A. Thermal energy
B. Kinetic energy
C. Chemical reaction
D. Nuclear reaction
Answer: C
3. What is the potential energy of a charge when it returns to the positive
terminal?
A. Infinite
B. Maximum
C. Zero
D. Negative
Answer: C

Capacitance
1. What is stored in a capacitor?
A. Magnetic field
B. Current
C. Electric potential energy
D. Resistance
Answer: C
2. What is the unit of capacitance?
A. Volt
B. Ampere
C. Farad
D. Joule
Answer: C
3. What is the formula for capacitance?
A. C = Q/V
B. C = V/Q
C. C = R/V
D. C = Q/I
Answer: A
4. Which of the following increases capacitance in a parallel-plate capacitor?
A. Decreasing area
B. Increasing distance
C. Increasing the area
D. Increasing resistance
Answer: C

5. What is the effect of inserting a dielectric between capacitor plates?

A. Reduces capacitance
B. Prevents energy storage
C. Increases capacitance
D. Increases resistance
Answer: C
6. What happens when a capacitor is discharged?
A. It stores more energy
B. Charge flows through a conductor
C. It attracts magnetic fields
D. Voltage increases
Answer: B
7. Which device commonly uses capacitors for rapid discharge?
A. Washing machine
B. Electric fan
C. Camera flash
D. Light bulb
Answer: C
8. What causes electrical breakdown in a capacitor?
A. Overheating
B. Exceeding voltage rating
C. Too much resistance
D. Low capacitance
Answer: B

Electrical Circuits, Resistance, and Power

1. Electric current is defined as:
A. Voltage × time
B. Charge per unit time
C. Resistance per volt
D. Charge per volt
Answer: B
2. What is the SI unit of current?
A. Ohm
B. Watt
C. Ampere
D. Volt
Answer: C
3. What is the direction of conventional current?
A. Electron to proton
B. Negative to positive terminal
C. Positive to negative terminal
D. Clockwise
Answer: C
4. Ohm’s Law is expressed as:
A. V = IR
B. I = VR
C. R = VI
D. V = I/R
Answer: A
5. Which of the following materials has the lowest resistivity?
A. Plastic
B. Copper
C. Glass
D. Wood
Answer: B
6. The formula for resistance using resistivity is:
A. R = ρA/L
B. R = ρL/A
C. R = L/ρA
D. R = A/ρL
Answer: B

7. Electric power can be calculated as:

A. P = I/V
B. P = IV
C. P = I/R
D. P = V/I
Answer: B
8. Which of the following is NOT a correct formula for power?
A. P = I²R
B. P = V²/R
C. P = V/I
D. P = IV
Answer: C
9. If a device uses 1.5 kW for 2 hours, the energy consumed is:
A. 3.0 kW
B. 3.0 W
C. 3.0 kWh
D. 0.75 kWh
Answer: C
Real-World Applications
1. What is the energy produced by a 1.4 × 10⁸ W generator in 1 hour?
A. 1.4 × 10⁶ J
B. 1.4 × 10⁹ J
C. 5.04 × 10¹¹ J
D. 3.6 × 10⁵ J
Answer: C

2. What is the current in a toaster with 120 V and 20 Ω?

A. 3 A
B. 5 A
C. 6 A
D. 7 A
Answer: C

3. What is the power consumed by the same toaster?

A. 240 W
B. 360 W
C. 600 W
D. 720 W
Answer: D
4. Hybrid cars use:
A. Only chemical energy
B. Only electric energy
C. Both chemical and electric energy
D. Solar energy
Answer: C
5. Electric heaters convert:
A. Heat into light
B. Light into sound
C. Electric energy into heat
D. Kinetic energy into electricity
Answer: C
6. A computer keyboard works using changes in:
A. Voltage
B. Capacitance
C. Resistance
D. Current
Answer: B

7. A utility bill charges based on:

A. Watts
B. Kilowatts
C. Resistance
D. Energy consumed (kWh)
Answer: D
8. Capacitors in sensors are sensitive to:
A. Temperature only
B. Light only
C. Spacing and materials
D. Battery type
Answer: C
9. A particle gains 4.0 × 10⁻¹⁸ J moving 5 cm in 8.0 × 10³ N/C. What is the charge?
A. 10.0 × 10⁻²² C
B. 1.0 × 10⁻²² C
C. 1.0 × 10⁻¹⁹ C
D. -1.0 × 10⁻¹⁹ C
Answer: B

10. Which component stores energy in an electric field?

A. Battery
B. Capacitor
C. Diode
D. Resistor
Answer: B
11. What increases when a dielectric is added?
A. Resistance
B. Voltage
C. Capacitance
D. Current
Answer: C

12. When a capacitor is charged, electrons:

A. Move to both plates
B. Move off both plates
C. Move from one plate to the other
D. Do not move
Answer: C
13. What happens to a capacitor when it is connected to a battery?
A. Nothing
B. It discharges
C. It loses all energy
D. It charges until voltage matches battery
Answer: D
14. A capacitor stores energy as:
A. Heat
B. Sound
C. Electric potential energy
D. Gravitational potential energy
Answer: C

15. The formula for electric energy is:

A. E = IVt
B. E = Pt
C. E = It/V
D. E = I/V
Answer: B
16. In a power formula, if I = 5 A and R = 2 Ω, then P =?
A. 10 W
B. 25 W
C. 50 W
D. 5 W
Answer: B

17. Which of the following has the highest resistance?

A. Short thick copper wire
B. Long thin copper wire
C. Short aluminum rod
D. Superconductor
Answer: B
18. What is the effect of increasing the area of capacitor plates?
A. Decrease capacitance
B. No effect
C. Increase capacitance
D. Increase resistance
Answer: C
Formulas and Quantities
• Electric Potential Energy in a Uniform Electric Field:
PE_electric = -qEd
• Electric Potential (V):
V = PE_electric / q
• Potential Difference (ΔV):
ΔV = ΔPE_electric / q
• In a Uniform Electric Field:
ΔV = -Ed
• Electric Potential due to a Point Charge:
V = k_C * q1 / r
• Potential Difference Between Two Points:
ΔV = k_C * q1 * (1/r2 - 1/r1)
• Superposition Principle for Electric Potential:
V_total = V1 + V2 + V3 + ...
• Capacitance Formula:
C = Q / ΔV
• Parallel-Plate Capacitor:
C = ε₀ * A / d
• Electric Current:
I=Q/t
• Ohm’s Law:
V = IR
• Resistance using Resistivity:
R=ρ*L/A
• Electric Power:
P = IV
P = I²R
P = V² / R
• Electrical Energy: E = Pt (or in kWh if P in kW and t in hours)
 Quantities and Their SI Units
Quantity Symbol Unit Unit Symbol
Electric potential energy PE or ΔPE joule J
Charge q or Q coulomb C
Electric field strength E newton/coulomb N/C
Distance (displacement) d meter m
Electric potential V volt V
Potential difference ΔV volt V
Coulomb's constant k_C N·m²/C² 8.99×10⁹ N·m²/C²
Radius/distance from r meter m
charge
Capacitance C farad F
Plate area (capacitor) A square meter m²
Plate separation d meter m
Permittivity of free space ε₀ C²/N·m² 8.85×10⁻¹²
C²/N·m²
Current I ampere A
Time t second s
Resistance R ohm Ω
Resistivity ρ ohm·meter Ω·m
Power P watt W
Electrical energy E joule or kilowatt- J or kWh
hour