Electricity – Notes, MCQs, Quiz & Worksheet

To calculate the resistivity (ρ) of the material, we use the formula:

R = ρ × (L / A)

Where:

• R = 20 ohms (resistance)
• L = 1 meter (length)
• A = πr² (cross-sectional area of the wire)
• r = 0.01 cm = 1 × 10⁻⁴ meters (radius)

Step-by-step calculation:

Calculate the area (A) of the wire's cross section:
A = π × (1 × 10⁻⁴)² = π × 10⁻⁸ m² ≈ 3.1416 × 10⁻⁸ m²

Rearrange the formula to solve for ρ:
ρ = R × (A / L)

Substitute the values:
ρ = 20 × (3.1416 × 10⁻⁸ / 1)

Calculate the resistivity:
ρ ≈ 20 × 3.1416 × 10⁻⁸ = 6.28 × 10⁻⁷ Ω·m

The resistance of a conductor depends on:

1. Length (L):Directly proportional to resistance.
2. Cross-sectional area (A): Inversely proportional to resistance.
3. Resistivity (ρ):Material property; higher resistivity means higher resistance.
4. Temperature (T): Generally, resistance increases with temperature.

Alloys are commonly used in electrical heating devices (like electric heaters, toasters, and irons) because of the following reasons:

1. High resistivity: Alloys have higher electrical resistivity than pure metals, which means they produce more heat when current flows through them.
2. Do not oxidize easily: Alloys like nichrome do not burn or oxidize easily at high temperatures, making them more durable than pure metals.
3. High melting point: They can withstand high temperatures without melting or deforming.
4. Stable resistance: The resistance of alloys does not change much with temperature, making heating performance more consistent and reliable.

Unit of Current:The SI unit of electric current is the ampere (A).

Definition :-  One ampere is the current when one coulomb of charge flows through a conductor in one second.
So,  1 ampere = 1 coulomb / 1 second

Resistance (R) = Resistivity (ρ) × (Length (L) / Area (A))

Given:-
Resistivity (ρ) = 2.8 × 10⁻⁸ ohm meter
Length (L) = 2 meters
Area (A) = 1.55 × 10⁻⁶ square meters

Substitute the values:
R = (2.8 × 10⁻⁸) × (2 / 1.55 × 10⁻⁶)
R = (5.6 × 10⁻⁸) / (1.55 × 10⁻⁶)
R ≈ 0.0361 ohms

Hence answer is  0.0361 ohms

The resistivity of alloys is generally higher than that of the pure metals from which they are made.

Why?

• In alloys, different types of atoms are mixed.
• These atoms disturb the regular structure of the metal lattice.
• This scatters electrons more, making it harder for electric current to flow.
• As a result, resistance increases, and hence resistivity is higher.

Example:

• Pure copper has low resistivity (good conductor).
• An alloy like nichrome (nickel + chromium) has much higher resistivity.

An electric circuit is a closed path through which electric current can flow. It usually includes a power source like a battery, wires to carry the current, and a device like a bulb or fan that uses the electricity.

If the path is complete (closed), electricity flows and the device works. If the path is broken (open), electricity cannot flow and the device does not work.

To find the number of electrons in one coulomb of charge:

Charge of one electron = 1.6 × 10⁻¹⁹ coulombs
Number of electrons = 1 ÷ (1.6 × 10⁻¹⁹)
= 6.25 × 10¹⁸ electrons

Hence  6.25 × 10¹⁸ electrons make up one coulomb of charge.

The resistance of a conductor depends on the following factors:

1. Length of the conductor (L): Resistance increases with length.
   (More length → More resistance)
2. Area of cross-section (A): Resistance decreases with a larger area.
   (More thickness → Less resistance)
3. Material of the conductor:  Different materials have different resistivities.
   (Some materials oppose current more than others)
4. Temperature: Resistance increases with temperature (for most conductors).

Metals are good conductors of electricity because they have a large number of free electrons (also called conduction electrons). These electrons are not tightly bound to atoms and can move freely through the metal. When a potential difference is applied, these free electrons flow easily, allowing electric current to pass.

Glass is a bad conductor (insulator) because its electrons are tightly bound to their atoms. It does not have free electrons available to move and carry electric current. As a result, electricity cannot flow through it easily.

In short:

• Metals have free-moving electrons  --->  Good conductors.
• Glass lacks free-moving electrons  ---->  Bad conductor.

Advantages of connecting electrical devices in parallel instead of in series:

1. Each device gets the full voltage of the battery:
   In parallel, every device gets the same voltage as the battery voltage, so all devices work properly.
2. Devices work independently:
   If one device stops working or is switched off, the others continue to work because they have their own separate paths.
3. Current is divided among devices:
   Total current is split according to resistance, preventing any one device from getting too much current.
4. Adding more devices does not reduce voltage:
   You can add more devices without reducing the voltage across each device.

Current will flow more easily through a thick wire than a thin wire of the same material when connected to the same source. 
Because a thick wire has a larger area of cross-section, so it offers less resistance to the flow of current. Lower resistance means more current can flow.

A battery maintains a potential difference by using chemical reactions to move electrons from one terminal to another. This creates a positive terminal and a negative terminal, allowing current to flow through a connected conductor.

Process:-

• The battery has two terminals: positive and negative.
• Chemical reactions inside the battery cause a buildup of electrons at the negative terminal and a deficit at the positive terminal.
• This creates an electric field between the terminals — a potential difference (voltage).
• When a conductor is connected, electrons flow from the negative to the positive terminal through the conductor, driven by this potential difference.

Given:
Current (I) = 1 A (Ampere)
Time (t) = 16 seconds

Charge of one electron (e) = 1.6 × 10⁻¹⁹ C (Coulombs)

Step 1: Calculate the total charge (Q) passing through the filament:

Q = I × t
Q = 1 A × 16 seconds
Q = 16 C (Coulombs)

Step 2: Calculate the number of electrons:

Number of electrons = Q / e
Number of electrons = 16 C / (1.6 × 10⁻¹⁹ C/electron)
Number of electrons = 1 × 10²⁰ electrons

Hence the number of electrons passing through the filament in 16 seconds is approximately 1 × 10²⁰ electrons.

Cell or Battery, These devices supply electrical energy and create the necessary potential difference to allow current to flow through a circuit.

If the resistance of an electrical component remains constant and the potential difference across it decreases to half of its original value, then the current flowing through it will also change.

According to Ohm’s Law:
Current (I) = Potential difference (V) ÷ Resistance (R)

Since resistance (R) is constant, if the potential difference (V) becomes half, then the new current will be:
I new = (1/2 × V) ÷ R = (1/2) × (V ÷ R) = (1/2) × I original

This means the current will become half of its original value.

Coils of electric toasters and electric irons are made of an alloy rather than a pure metal due to following reasons:

1. Alloys have higher resistance than pure metals, so they produce more heat when electric current passes through them, which is useful for heating devices.
2. Alloys do not melt easily,  they have higher melting points, so the coils can withstand high temperatures without melting.
3. Alloys are more durable and strong,so the coils last longer under repeated heating and cooling.

The cord of an electric heater does not glow because it is made of a material with low resistance, so it does not heat up much.

The heating element glows because it is made of a material with high resistance, which causes it to get very hot and produce light when current passes through it.

The rate at which energy is delivered by a current is called power.

Power (P) = Voltage (V) × Current (I)

So, the rate of energy delivery depends on both the voltage and the current.

The energy given to each coulomb of charge passing through a 6 V battery is calculated using the formula:
Energy = Voltage × Charge

Here, the voltage is 6 V and the charge is 1 coulomb.
Energy = 6 V × 1 C = 6 Joules

So, the energy given to each coulomb of charge is 6 joules.

Given:
Charge (Q) = 96000 coulombs
Potential difference (V) = 50 volts

Formula:
Heat generated (H) = Voltage (V) × Charge (Q)
H = 50 × 96000 = 4800000 joules

Hence the heat generated is 4800000 joules (4.8 million joules).

Given:
Resistance (R) = 20 ohms
Current (I) = 5 amperes
Time (t) = 30 seconds

Formula:
Heat developed (H) = I² × R × t
H = 5² × 20 × 30 = 25 × 20 × 30 = 15000 joules

Hence heat developed in 30 seconds = 15000 joules

To find the maximum resistance that can be made using five resistors, each of 1/5 Ω, you should connect all the resistors in series, because resistances add up in series.

The formula for total resistance in a series connection is:

R_total = R1 + R2 + R3 + R4 + R5

Since each resistor has a value of 1/5 Ω, we can calculate:

R_total = 1/5 + 1/5 + 1/5 + 1/5 + 1/5

R_total = 5 × 1/5 = 1 Ω

Hence the maximum resistance that can be made using five resistors, each of 1/5 Ω, is 1 Ω.

When we say that the potential difference between two points is 1 volt (1 V), it means that 1 joule of work is done to move 1 coulomb of charge from one point to the other.

In simple words:
1 volt = 1 joule / 1 coulomb