- Charges in Nature
- Methods of Charging
- Coulomb’s Law
- Electric Field
- Electric Circuits
- Ohm’s Law
- Resistors
- Meters
- Safety
- Summary
Welcome, dear student! Unit 4 is one of the biggest and most important units in Grade 10 Physics. We will learn about electricity, which is part of our daily life in Ethiopia. When you turn on a light, charge your phone, or use a refrigerator, electricity is at work. This unit has two main parts. First, static electricity, where charges stay in one place. Second, current electricity, where charges flow through wires. Let us learn each concept deeply from your textbook.
4.1 Charges in Nature
Have you ever rubbed a plastic pen on your hair and then brought it near small pieces of paper? The paper jumps up and sticks to the pen! Why does this happen? It happens because of electric charge. Let me explain this deeply.
Types of Electric Charges
In nature, there are exactly two types of electric charges. Your textbook explains this clearly.
Positive charge (+) — This is the charge on a proton.
Negative charge (−) — This is the charge on an electron.
These charges are fundamental properties of matter. Every atom is made of protons (positive), neutrons (no charge), and electrons (negative). Normally, an atom has equal numbers of protons and electrons, so the total charge is zero. We say the atom is neutral. But when an object gains or loses electrons, it becomes charged.
How Objects Become Charged
Protons are stuck deep inside the nucleus of an atom. They cannot move easily. But electrons are on the outside of the atom, and they can be transferred from one object to another. This is the key idea.
- If an object loses electrons, it has more protons than electrons. It becomes positively charged.
- If an object gains electrons, it has more electrons than protons. It becomes negatively charged.
Electric charge is NOT created or destroyed. It is only transferred from one object to another. This is called the law of conservation of charge. If one object gains 5 electrons, another object must lose exactly 5 electrons. The total charge in the universe stays the same.
Basic Properties of Electric Charges
There are three basic properties you must know for your exam:
1. Like charges repel each other. If you bring two positive charges close, they push each other away. Two negative charges also push each other away.
2. Unlike charges attract each other. A positive charge and a negative charge pull each other together.
3. Charged objects attract neutral objects. If you bring a charged plastic pen near a neutral piece of paper, the paper is attracted. This happens because the charge on the pen rearranges the charges in the paper (a process called induction, which we will learn later).
$$ Q = ne $$
Q = total charge | n = number of electrons transferred | e = charge of one electron
e = \( 1.6 \times 10^{-19} \) C (Coulombs)
This formula tells us that charge comes in small packets. You cannot have half an electron’s worth of charge. The smallest unit of charge is the charge of one electron (\(1.6 \times 10^{-19}\) C). All charges are whole number multiples of this value. The SI unit of charge is the Coulomb (C).
- Two types of charges: positive (+) and negative (-)
- Like charges repel, unlike charges attract
- Charges are transferred by moving electrons, not protons
- Losing electrons = positive charge; Gaining electrons = negative charge
- SI unit of charge = Coulomb (C)
- Charge of one electron \( e = 1.6 \times 10^{-19} \) C
- Charge is conserved (cannot be created or destroyed)
Practice Questions — Charges in Nature
Explanation: The glass rod became positively charged because it LOST electrons (not because it gained protons). Protons cannot move because they are locked in the nucleus. The electrons transferred from the glass to the silk. The silk gained electrons and became negatively charged. Charge was conserved. Option C is wrong because charge cannot be created.
Explanation: Use \( Q = ne \). Here \( Q = -3.2 \times 10^{-19} \) C and \( e = 1.6 \times 10^{-19} \) C. So \( n = Q/e = (-3.2 \times 10^{-19}) / (1.6 \times 10^{-19}) = -2 \). The negative sign just tells us the charge is negative (excess electrons). The number of excess electrons is 2.
4.2 Methods of Charging a Body
Now we know that charges are transferred by moving electrons. But how exactly do we transfer them? Your textbook explains three methods. Let us look at each one deeply.
1. Charging by Friction
This is the simplest method. When you rub two different materials together, electrons are transferred from one to the other. The material that holds electrons more strongly pulls them from the other material. For example, when you rub a plastic pen with your hair, electrons move from your hair to the pen. The pen becomes negative (gained electrons) and your hair becomes positive (lost electrons).
2. Charging by Conduction (Contact)
In this method, a charged object touches a neutral object. Electrons flow directly from one to the other. For example, if a negatively charged metal rod touches a neutral metal sphere, electrons flow from the rod to the sphere. The sphere becomes negatively charged, and the rod loses some of its charge. The key point is that both objects end up with the same type of charge after contact.
3. Charging by Induction
This method is the most interesting and is frequently tested in exams. In induction, a charged object is brought near (but does NOT touch) a neutral object. The charges in the neutral object are rearranged without any direct contact.
Step 1: Bring a negatively charged rod near a neutral metal sphere. The negative charges (electrons) in the sphere are repelled to the far side. The near side becomes positive.
Step 2: Ground the sphere (connect it to the Earth with a wire). The repelled electrons flow into the Earth.
Step 3: Remove the ground connection. The sphere now has a net positive charge (it lost electrons to the Earth).
Step 4: Remove the charged rod. The positive charge spreads evenly over the sphere.
Result: The sphere is now positively charged, and it never touched the rod!
Conduction: Objects touch. They get the same type of charge.
Induction: Objects do NOT touch. They get opposite types of charge.
Practice Questions — Methods of Charging
Explanation: The positive rod attracts electrons in the sphere to the near side. When grounded, electrons flow FROM the Earth INTO the sphere (because the positive rod is pulling them). When the ground is removed, those extra electrons are trapped. When the rod is removed, the sphere has excess electrons, so it is negatively charged. Induction always gives the opposite charge!
Explanation: This is charging by conduction (contact). Electrons flow from the negatively charged object to the neutral object. The neutral object gains electrons and becomes negative. In conduction, both objects end up with the same type of charge.
4.3 The Electroscope and 4.4 Electrical Discharge
The Electroscope
An electroscope is a device used to detect the presence and type of electric charge on an object. It consists of a metal rod with a metal ball at the top and two thin metal leaves (usually gold foil) at the bottom, all inside a glass case.
When a charged object touches the metal ball, charge flows down the rod to the leaves. Both leaves get the same type of charge. Since like charges repel, the leaves spread apart. The more charge, the wider they spread. If the leaves do not move, the object is neutral.
Electrical Discharge
When a large amount of charge builds up on an object, it can suddenly flow to another object or to the ground. This sudden flow of charge is called electrical discharge. Lightning is a dramatic example of electrical discharge. Charge builds up in clouds and then suddenly jumps to the ground or to another cloud.
Electric shock happens when charge flows through your body to the ground. This is dangerous and can be fatal. That is why buildings use lightning conductors (thick metal rods connected to the ground) to safely discharge lightning strikes.
4.5 Coulomb’s Law of Electrostatics
We know that charges exert forces on each other (like charges repel, unlike charges attract). But how strong is that force? Coulomb’s Law gives us the exact mathematical answer. This is one of the most important laws in physics and is heavily tested in exams.
The force between two point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them.
$$ F = k \frac{q_1 q_2}{r^2} $$
F = electrostatic force (N) | k = Coulomb’s constant \( = 9 \times 10^9 \) Nm2/C2
q1, q2 = magnitudes of the two charges (C) | r = distance between them (m)
Let me explain each part of this formula deeply so you never forget it.
“Directly proportional to the product of charges” means if you double one charge, the force doubles. If you triple both charges, the force becomes 9 times larger (\(3 \times 3 = 9\)). Larger charges mean stronger force.
“Inversely proportional to the square of the distance” means if you double the distance, the force becomes \(1/4\) (not 1/2). If you triple the distance, the force becomes \(1/9\). The “square” makes the force drop very quickly as the charges move apart.
The formula gives the magnitude of the force (always positive). You must determine the direction separately using the rule: like charges repel, unlike charges attract. Some students put negative signs for the charges in the formula and get a negative force. This is often confusing. It is safer to use the absolute values of charges in the formula, and then state the direction separately.
Problem: Two charges of \(3 \times 10^{-6}\) C and \(5 \times 10^{-6}\) C are placed 0.2 m apart in a vacuum. What is the force between them?
$$ F = k \frac{q_1 q_2}{r^2} = (9 \times 10^9) \frac{(3 \times 10^{-6})(5 \times 10^{-6})}{(0.2)^2} $$
$$ F = (9 \times 10^9) \frac{15 \times 10^{-12}}{0.04} = (9 \times 10^9) \times 375 \times 10^{-12} $$
$$ F = \textbf{3.375 N} $$
Since both charges are positive, the force is repulsive. The charges push each other away.
- Coulomb’s Law: \( F = k q_1 q_2 / r^2 \)
- \( k = 9 \times 10^9 \) Nm2/C2
- Force is proportional to \( q_1 \times q_2 \)
- Force is inversely proportional to \( r^2 \) (NOT just r)
- Distance must be in metres (convert cm to m if needed)
- Use absolute values for charges, find direction separately
Practice Questions — Coulomb’s Law
Explanation: Since \( F \propto 1/r^2 \), if r becomes 2r, then \( F \propto 1/(2r)^2 = 1/4r^2 \). The force becomes 1/4 of the original. This is a very common exam question. Many students wrongly answer “halves” because they forget the SQUARE.
Explanation: \( F = (9 \times 10^9) \times (2 \times 10^{-6}) \times (2 \times 10^{-6}) / (0.1)^2 = (9 \times 10^9) \times (4 \times 10^{-12}) / 0.01 = 36 \times 10^{-3} / 0.01 = 36 \times 10^{-1} = \) 3.6 N. Since both are positive, the force is repulsive.
4.6 The Electric Field
How does a charge “know” that another charge is nearby? How does the force travel across the space between them? The answer is the electric field. A charge creates an invisible “field” around itself. Any other charge placed in this field feels a force.
Electric field is the region around a charged object where another charge experiences an electric force. The strength of the field at a point is the force per unit positive charge placed at that point.
$$ E = \frac{F}{q} $$
E = electric field strength (N/C) | F = force on the test charge (N) | q = test charge (C)
The electric field points away from positive charges and towards negative charges. We draw electric field lines to show the direction of the field. These lines start on positive charges and end on negative charges. The closer the lines are together, the stronger the field.
Practice Questions — Electric Field
Explanation: \( E = F/q = 0.1 / (2 \times 10^{-5}) = 0.1 / 0.00002 = 5000 \) N/C. Direct application of the formula.
Explanation: By convention, electric field lines point away from positive charges and towards negative charges. If you place a small positive test charge near a positive source charge, the test charge is repelled (pushed away). So the field direction is outwards.
4.7 Electric Circuits
Now we move from static electricity to current electricity. In static electricity, charges stay in place. In current electricity, charges flow continuously through a path. This path is called an electric circuit.
An electric circuit is a closed path through which electric current flows. It must have a source of energy (like a battery), a conducting path (wires), and usually a device that uses the energy (like a bulb).
Essential Parts of a Circuit
| Component | Symbol | Function |
|---|---|---|
| Cell/Battery | | | (long/short lines) | Provides energy (drives current) |
| Resistor | Zigzag line | Opposes current flow (uses energy) |
| Switch | Dot with a line | Opens or closes the circuit |
| Ammeter | A in a circle | Measures current |
| Voltmeter | V in a circle | Measures voltage |
| Connecting wires | Straight lines | Carry current |
Types of Circuits
Open circuit: The path is broken (switch is open). No current flows. The bulb is off.
Closed circuit: The path is complete (switch is closed). Current flows. The bulb is on.
Short circuit: A low-resistance path bypasses the normal load. Very large current flows, which can cause fire or damage. This is very dangerous.
4.8 Current, Voltage, and Ohm’s Law
This is the most important section of the entire unit. You MUST understand these three concepts perfectly.
What is Electric Current?
Electric current is the rate of flow of electric charge through a conductor. Think of it like water flowing through a pipe. The more water flows per second, the greater the current.
$$ I = \frac{Q}{t} $$
I = current (Ampere, A) | Q = charge (Coulomb, C) | t = time (seconds, s)
The SI unit of current is the Ampere (A). One Ampere means one Coulomb of charge flows past a point every second. Conventional current direction is from positive to negative (outside the battery), but in reality, electrons flow from negative to positive.
What is Voltage (Potential Difference)?
Voltage is the energy needed to move a unit charge from one point to another. It is the “push” that drives current through a circuit. Think of voltage like water pressure in a pipe. Higher pressure pushes more water. Higher voltage pushes more current.
$$ V = \frac{W}{Q} $$
V = voltage (Volt, V) | W = work done or energy (Joule, J) | Q = charge (C)
The SI unit of voltage is the Volt (V). One Volt means one Joule of energy is needed to move one Coulomb of charge.
What is Resistance?
Resistance is the opposition to the flow of current in a conductor. Every material resists current to some degree. A wire with high resistance allows less current to flow. A wire with low resistance allows more current.
The SI unit of resistance is the Ohm (symbol: \(\Omega\)). Factors that affect resistance: length of wire (longer = more resistance), cross-sectional area (thicker = less resistance), material (some materials resist more than others), and temperature.
Ohm’s Law
Now we connect all three quantities with one of the most famous laws in physics.
At constant temperature, the current through a conductor is directly proportional to the voltage across it.
$$ V = IR $$
V = voltage (V) | I = current (A) | R = resistance (\(\Omega\))
This formula can be rearranged into three forms:
\( V = IR \) (find voltage)
\( I = V/R \) (find current)
\( R = V/I \) (find resistance)
Ohm’s law means: if you increase the voltage, the current increases (if resistance stays the same). If you increase the resistance, the current decreases (if voltage stays the same).
Problem: A 12 V battery is connected to a resistor of 4 \(\Omega\). What current flows through the resistor?
$$ I = \frac{V}{R} = \frac{12}{4} = \textbf{3 A} $$
A current of 3 Amperes flows through the resistor.
Cover the quantity you want to find with your finger:
Practice Questions — Current, Voltage, and Ohm’s Law
Explanation: First convert time to seconds: 2 minutes = 120 s. Then \( I = Q/t = 60/120 = 0.5 \) A. Common mistake: forgetting to convert minutes to seconds. If you used 2 minutes directly, you would get 30 A, which is wrong!
Explanation: \( V = IR = 2 \times 10 = 20 \) V. Direct application of Ohm’s law.
Explanation: From \( I = V/R \), if V becomes 3V, then I becomes \( 3V/R = 3I \). Current is directly proportional to voltage (at constant resistance). This is exactly what Ohm’s law states.
4.9 Combination of Resistors in a Circuit
In real circuits, we rarely have just one resistor. They are connected in different ways. There are two main methods: series and parallel. You must know how to find the total resistance for each type. This is heavily tested in exams.
Resistors in Series
In a series circuit, resistors are connected one after another along a single path. The current has only one way to flow — through each resistor in turn.
$$ R_T = R_1 + R_2 + R_3 + \dots $$
In series, total resistance is the SUM of individual resistances.
Key facts about series circuits:
- Current is the SAME through all resistors
- Voltage is shared: \( V_T = V_1 + V_2 + V_3 \)
- Total resistance is always greater than any single resistance
- If one resistor breaks, the entire circuit stops working
Resistors in Parallel
In a parallel circuit, resistors are connected side by side. The current has multiple paths to flow through. Each resistor gets its own branch.
$$ \frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \dots $$
For two resistors: \( R_T = \frac{R_1 \times R_2}{R_1 + R_2} \)
In parallel, total resistance is the RECIPROCAL SUM. Always smaller than the smallest individual resistor.
Key facts about parallel circuits:
- Voltage is the SAME across all branches
- Current is shared: \( I_T = I_1 + I_2 + I_3 \)
- Total resistance is always less than the smallest individual resistance
- If one branch breaks, other branches still work
Problem: Three resistors of 4 \(\Omega\), 6 \(\Omega\), and 10 \(\Omega\) are connected in series to a 20 V battery. Find the total resistance, the current, and the voltage across the 6 \(\Omega\) resistor.
Total resistance: \( R_T = 4 + 6 + 10 = \) 20 \(\Omega\)
Current: \( I = V/R_T = 20/20 = \) 1 A (this same current flows through all resistors)
Voltage across 6 \(\Omega\): \( V = IR = 1 \times 6 = \) 6 V
Problem: Two resistors of 6 \(\Omega\) and 12 \(\Omega\) are connected in parallel to a 12 V battery. Find the total resistance and the total current.
Total resistance: \( R_T = (6 \times 12) / (6 + 12) = 72/18 = \) 4 \(\Omega\)
Total current: \( I = V/R_T = 12/4 = \) 3 A
Note: 4 \(\Omega\) is less than both 6 \(\Omega\) and 12 \(\Omega\). Parallel always reduces total resistance!
For parallel resistors, students often add them directly (like series). NEVER add parallel resistors directly! Always use the reciprocal formula or the product-over-sum formula for two resistors. Also, remember that the total parallel resistance is always LESS than the smallest individual resistance.
Practice Questions — Combination of Resistors
Explanation: \( R_T = (4 \times 12) / (4 + 12) = 48/16 = 3 \, \Omega \). Option A (16) is the series answer (wrong). The correct parallel answer (3) is less than both 4 and 12, which confirms it is correct.
Explanation: In series: \( R_T = 6 + 6 + 6 = 18 \, \Omega \). Simple addition for series. If they were parallel, it would be \( 1/R_T = 1/6 + 1/6 + 1/6 = 3/6 \), so \( R_T = 2 \, \Omega \). Always check whether the question says series or parallel!
Explanation: In a parallel circuit, the total current equals the sum of the branch currents: \( I_T = I_1 + I_2 = 2 + 3 = 5 \) A. Current splits at the junction and recombines. This is the opposite of series, where current is the same through all components.
4.10 Voltmeter and Ammeter Connection in a Circuit
To measure electricity in a circuit, we use two meters. They must be connected differently, and this is a very common exam question.
Ammeter
An ammeter measures current. Since current flows through the circuit, the ammeter must be placed in the path of the current. This means it is connected in series with the component whose current you want to measure.
- Connected in SERIES
- Has very LOW resistance (so it does not reduce the current it is measuring)
- If it had high resistance, it would change the current in the circuit
Voltmeter
A voltmeter measures voltage (potential difference) across a component. It must be connected across the component, not in the path. This means it is connected in parallel with the component.
- Connected in PARALLEL with the component
- Has very HIGH resistance (so no current flows through it instead of the component)
- If it had low resistance, it would act like a short circuit and draw all the current
Practice Questions — Meter Connections
Explanation: The voltmeter is connected in parallel. If it had low resistance, most of the current would flow through the voltmeter (the path of least resistance) instead of through the component. This would give a wrong reading and damage the circuit. High resistance ensures almost no current goes through the voltmeter.
Explanation: Current is the same at every point in a series path. By placing the ammeter in series with the resistor, the exact current flowing through the resistor also flows through the ammeter. If connected in parallel, the current would split and the ammeter would not measure the correct current through the resistor.
4.11 Electrical Safety and 4.12 Electric Projects
Your textbook includes important discussions about electrical safety in Ethiopia. Let me share the key points because they often appear in exam questions.
Electrical Safety
Electricity is very useful but also very dangerous. In Ethiopia, electrical accidents are common due to improper wiring, overloaded circuits, and lack of safety equipment. Here are the main safety measures:
- Fuses: A fuse is a short piece of wire that melts and breaks the circuit if too much current flows. This prevents fires and damage.
- Earth/Ground connection: The metal casing of appliances is connected to the ground. If a fault occurs, the current flows safely to the ground instead of through a person.
- Insulation: Wires are covered with plastic or rubber to prevent electric shocks.
- Do not overload circuits: Plugging too many appliances into one socket can cause overheating and fire.
- Keep water away from electricity: Water conducts electricity. Never touch electrical appliances with wet hands.
- Switch off before repairing: Always turn off the main switch before working on any electrical device.
Complete Unit Summary — Exam Preparation
Well done, dear student! Unit 4 is the longest unit in Grade 10 Physics, but if you understand the formulas and concepts below, you will do very well. Here is your complete summary.
Charge Quantization: \( Q = ne \)
Coulomb’s Law: \( F = k q_1 q_2 / r^2 \)
Electric Field: \( E = F/q \)
Current: \( I = Q/t \)
Voltage: \( V = W/Q \)
Ohm’s Law: \( V = IR \)
Power: \( P = IV = I^2R = V^2/R \)
Series Resistance: \( R_T = R_1 + R_2 + R_3 \)
Parallel Resistance: \( 1/R_T = 1/R_1 + 1/R_2 + 1/R_3 \)
Two Parallel Resistors: \( R_T = R_1 R_2 / (R_1 + R_2) \)
Energy: \( E = Pt = IVt \)
- Two types of charges: positive and negative
- Like charges repel, unlike charges attract
- Charging by friction, conduction (same charge), and induction (opposite charge)
- Electroscope detects charge by leaf separation
- Coulomb’s Law: force depends on charges and square of distance
- Electric field points away from positive, towards negative
- Current = rate of flow of charge (I = Q/t)
- Voltage = energy per unit charge (V = W/Q)
- Ohm’s Law: V = IR (at constant temperature)
- Series: same current, voltage divides, resistances add
- Parallel: same voltage, current divides, reciprocal resistances add
- Ammeter: series, low resistance
- Voltmeter: parallel, high resistance
- Fuses protect circuits by melting at high current
✓ Always convert units: cm to m, minutes to seconds, mA to A, kV to V
✓ Coulomb’s Law: Remember the “square” in the denominator. Doubling distance = 1/4 force
✓ Ohm’s Law: Use the triangle trick to avoid mixing up V, I, and R
✓ Series vs. Parallel: Series = add resistances. Parallel = reciprocal sum (never add directly!)
✓ Parallel total R is always LESS than the smallest resistor
✓ Meter connections: Ammeter = series, Voltmeter = parallel (never mix them up!)
✓ Induction gives opposite charge, Conduction gives same charge
✓ Charge quantization: Number of electrons is always a whole number
✓ Read circuit diagrams carefully before solving — trace the path of current
Unit 4 is the foundation for all electrical studies in Grade 11 and 12, and for anyone interested in electrical engineering. The concepts of Ohm’s law, series and parallel circuits, and Coulomb’s law will follow you throughout your physics education. Practise as many numerical problems as you can, especially on series/parallel resistors and Ohm’s law. Good luck with your exam, dear student!