Electrical Quantities

Electrostatic charges are created when electrons are transferred between objects by rubbing.

This can cause sparks or small electric shocks when touching an earthed object. Lightning is a dramatic example of static electricity.

There are two types of charges: like charges repel, opposite charges attract. Charges build up on insulators like plastic and stay static, while on conductors like metals, they flow away to neutralise.

Both conductors and insulators are useful. Electric charges create an electric field that exerts a force on nearby charges, similar to a magnetic field.

The Wonders of Static Electricity

We get to experience static electricity in our daily lives in many ways. Some are listed below:

• You may notice tiny sparks when taking off clothes made of synthetic fibres.
• Ever realised a small shock when getting out of a car? An electrostatic charge builds up on the car, and then discharges through you when you touch the metal door.
• When you rub a balloon on clothes you may observe how it sticks to the wall or to the ceiling
• When you rub a plastic ruler with a cloth, both are likely to become electrically charged.

These are wonders of static electricity.

Positive and negative charges

Now let's look at why these phenomena occur. Here is an example:

Try this using the simulation above-

1. Rub the balloon with the cloth so that both become charged.
2. Bring the balloon nearer to the cloth. Notice how it moves towards the cloth. This is an electrostatic attraction.
3. Now, rub the second balloon in the same way and bring it close to the first one. What just happened? the first balloon moves away. This is electrostatic repulsion.

The above example suggests that there are two types of static electricity:

1. Positive charge
2. Negative charge

From the example below we can also say something about the forces on the forces exerted by electric charges on each other:

1. Same charges repel
2. Opposite charges attract

Electric fields

It doesn’t matter whether an object is charged or uncharged: a single charged object can affect both without touching it.

We say that there is an electric field around a charged object. Any other charged object placed in this field will experience a force exerted on it.

Charging by induction

As seen before charged objects can attract uncharged objects. Try this: Scatter some tiny pieces of paper on a desk.

1. Rub a polythene rod on a woollen cloth.
2. Both the charged rod and the charged cloth will attract the paper.
3. This is the same effect as rubbing a balloon on clothes and sticking on a wall
4. An uncharged object (the wall) is attracted by the charged one (the balloon)

Wondering how this happens?

Let’s see how:

1. Suppose the balloon has a positive charge.
2. It must be attracted to a negative charge in the wall
3. The wall itself is neutral, as it is made up of positively and negatively charged particles.
4. When the balloon is brought close to the wall its electrons moves towards the balloon, because they are attracted by it.
5. This brings the negatively charged particles towards the surface of the wall.
6. This effect is enough to give the surface of the wall a negative charge.

We say that a negative charge has been induced on the wall. This is entire process is known as charging by induction.

Representing an electric field

A charged object is surrounded by an electric field. If another charged object moves into this electric field it experiences a force being exerted on it. This causes the objects to attract or repel each other.

We can represent an electric field by lines of force (or electric field lines) (this is similar to magnetic field lines) the lines of force are shown coming out of a positive charge and going into a positive charge.

This is because the lines indicate the direction of the force on a positive charge placed in the field. A positive charge is repelled by another positive charge and is attracted by a negative charge.

When two oppositely charged objects are placed close to each other they attract one another. Similarly, two objects with the same charge repel each other.

When two oppositely charged parallel plates are brought together the lines of forces between the plates are straight and parallel to one another except at the edges.

Electric current

An electric current is the rate at which electric charge flows in a circuit. When a circuit is complete, an electric current flows.

An electric current always flows from the positive terminal of the supply to the negative terminal of the supply

The unit of current is Ampere (also known as Amps and also just A).

Current can be calculated using the following formula:

I = Q / t

Where I = Current (A or C/s), Q = Charge (Coulombs) and t = time (seconds).

To measure current in a circuit, we use something called an ammeter, this device is used in series with the component(s). There are two types of ammeters: analogue and digital.

A suitable range (senstivity) must be chosen when measuring current using an ammeter, for example if you know the current is low, use a range from 10 mA (milli amps) to 100 mA.

If you know the current is going to be high, use a higher range like 1 A to 10 A.

Direct and alternating current

Electric current in series and parallel circuits

Electromotive force and potential difference

Electromotive force

There is a special term for the voltage across a cell. It is known as an electro motive force (e.m.f) of the cell and it is also measured in volts.

Any component that pushes a current around it has an e.m.f

Examples of components having an e.m.f are:

• Cells
• Batteries
• Power supplies
• Dynamos

Formula for Electromotive force:

E = W / Q

Where:

• E = Electromotive force (in volts, V)
• W = Work done or energy supplied by the source (in joules, J)
• Q = Charge moved (in coulombs, C)

Potential Difference

Potential difference in an electrical circuit indicates that there is a difference in electrical potential across a circuit component (such as a battery).

Potential difference is measured in volts (V) and the term voltage is also used instead of potential difference.

Potential difference is measured using a voltmeter.

Formula for measuring potential difference:

V = W / Q

Where:

• V = Potential difference (in volts, V)
• W = Work done or energy transferred (in joules, J)
• Q = Charge moved (in coulombs, C)

Resistance

Resistance is the opposition of a conductor to a current. When a voltage is applied, electrons tend to move more easily in some conductors than others. I

t’s unit is ohms (Ω).

Here is where the term ‘opposition’ comes. Certain conductors oppose the flow of electrons and thus have a higher resistivity (see the section below on resistivity)

A good conductor has low electrical resistance whereas a poor conductor has a high electrical resistance.

The resistance of a wire of a certain material depends upon three factors:

1. It increases as the length of a wire increases,
2. It increases as the cross-sectional area of a wire decreases,
3. It depends on the material through which it is passing the material

V=I × R

R= V / I

Where:

• R = Resistance (in ohms, Ω)
• V = Potential difference (in volts, V)
• I = Current (in amperes, A)

Resistivity

It has been proven that the resistance R of a wire of a given material is:

• Directly proportional to its length: This means that the greater the length of the wire, the greater its resistance would be.
• Inversely proportional to its cross-sectional area: This means that the shorter the diameter (thickness) of a wire, the greater its resistance shall be.

We use the formula:

R = (ρ × L) / A

Where:

• R = Resistance (in ohms, Ω)
• ρ (rho) = Resistivity of the material (in ohm-metres, Ω·m)
• L = Length of the conductor (in metres, m)
• A = Cross-sectional area of the conductor (in square metres, m²)

I–V Graphs: Ohm’s Law (Current–Voltage Graphs)

An I–V graph shows how the current (I) changes with voltage (V) for different materials or components. Let’s look at what this means for different types of conductors.

Metallic Conductors (like metals and some alloys)

• The graph for a metallic conductor (like in Figure 4.2.29a) is a straight line through the origin (0,0).
• This means that current (I) increases at the same rate as voltage (V) — if you double the voltage, the current also doubles.
• This shows a directly proportional relationship: I ∝ V.
• These materials obey Ohm’s Law.

Ohm’s Law

Ohm’s Law says:

"The current in a metallic conductor is directly proportional to the potential difference (voltage) across its ends, as long as the temperature and other conditions stay the same."

• Conductors that follow Ohm’s Law are called ohmic or linear conductors.
• Since I ∝ V, the ratio V/I stays the same — this ratio is the resistance.
• On the graph, this constant ratio is shown by the slope (gradient) of the line.

Filament lamp

The I-V graph for a filament lamp, such as a bulb represents an “S” shape.

At low voltages, the current is relatively small because the filament has high resistance when it is cold.

As the voltage increases, the lamp heats up, reducing its resistance, and the current rises more steeply.

Diode

A diode’s typical I-V graph shows that it allows current to pass in one direction but almost blocks it in the opposite direction.

It has low resistance when connected forward, allowing current flow, but high resistance when reversed.

This characteristic makes it a non-ohmic conductor, conducting in one direction only.

Electrical Working

Electric circuits transfer energy from a power source (e.g., battery) to circuit components and eventually dissipate it into the surroundings. The source provides electrical energy, which powers the components. The components utilize or convert this energy into various forms (e.g., heat, light) before it is released into the surroundings

P = W / t

Power = energy transferred / time taken

Where

• W = Work done in Joules
• P = Power
• t = time taken in seconds

The unit of Power is Watts (W), also known as Joules per second (J/s)

Another formula for power is:

Power = Voltage × Current

P=V × I

To calculate energy used, we use the following formula

Energy = Power × Time = Voltage × Current × Time

E= P × t = V × I × t

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