CURRENT ELECTRICITY

Site:	Newgate University Minna - Elearning Platform
Course:	General Physics II
Book:	CURRENT ELECTRICITY

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Date:	Monday, 2 November 2026, 11:45 PM

1. Introduction
2. RESISTANCE AND RESISTIVITY
3. OHM'S LAW AND SIMPLE DC CIRCUIT ANALYSIS
4. ENERGY DISSIPITATION IN RESISTORS

1. Introduction

Current electricity is the branch of physics that deals with the flow of electric charges (usually electrons) through a conductor such as a wire. It occurs when there is a continuous path, called an electric circuit, and a source of electrical energy, such as a battery or generator, that provides a potential difference (voltage) to drive the charges.

Electric current is responsible for the operation of electrical devices such as bulbs, fans, televisions, computers, and many other appliances used in everyday life. The study of current electricity includes concepts such as electric current, voltage, resistance, electrical power, and electric circuits, which are essential for understanding how electrical systems work.

Definition: Electric current is rate of flow of electric charge through a conductor. It occurs when there is a continuous movement of charges (usually electrons) in a material. The conventional direction of current is taken as the direction in which positive charges would flow, from the positive terminal to the negative terminal of a power source.

Mathematical Expression I = Q / t

Where:

I = current (A)

Q = quantity of charge (C)

t = time (s)

1.1 Components of Electric Current

1.2 Electric Charge

Electric charge is a fundamental property of matter responsible for all electrical phenomena.

Types of Electric Charge

There are two types of electric charge:

1. Positive charge: Carried by protons

2. Negative charge: Carried by electrons

Like charges repel each other, while unlike charges attract each other. The SI unit of electric charge is the coulomb (C). The charge of a single electron is approximately: [ e = 1.6 ^-19C]

1.3 Ohm’s Law

It states that the current flowing through a conductor is directly proportional to the potential difference across it, provided temperature and other physical conditions remain constant. V = IR Where: -

I = current (A)

V= potential difference (V)

R = resistance (Ω)

2. RESISTANCE AND RESISTIVITY

2.0 Resistance (R) Resistance is the opposition to the flow of electric current in an electric circuit. It is a measure of the difficulty to pass an electric current through a circuit. From Ohm’s law,

Therefore, one ohm is the resistance of a conductor in which a current of one ampere flows through it when a potential difference of one volt is maintained between its two ends. Examples:

1. If the resistance of a circuit is 12Ω and the current of 4A passes through it calculate the potential difference.

2. The electric fan takes a current of 0.5A when operated on a 200V supply. Find the resistance.

2.1 Factors Affecting the Resistance

The resistance of a conductor depends on the following factors:

(i) Length: The resistance of a conductor of uniform cross-sectional area is directly proportional to its length. R µ l

(ii) Area: The resistance of a conducting wire is inversely proportional to its area.

(iii) Temperature: The resistance of a conductor varies directly with its temperature.

For Ohmic conductors, R µ T

(iv) Type of material: The resistance of a conductor depends upon the material of which it is made.

Experiments show that the resistance R of an ohmic conductor maintained at a constant temperature is related to its length (l) and its cross-sectional area (A) by the expression:

where ρ is a constant of proportionality known as resistivity.

2.2 Resistivity

Resistivity is a measure of how much a material resists the flow of electrical charge through it. It is defined as the ratio of the electric field strength to the current density in a material.

Resistivity is an intrinsic property of a material and depends on the material’s temperature and other factors.

SI unit of resistivity is Ohm-meter (Ωm).

where ρ is the resistivity of the conductor in ohm-meter

R is the resistance in ohms

A is the surface area of the conductor

l is the length of the conducting wire

Examples

1. What is the resistivity of a cylindrical material wire whose 1m length has a resistance of 2Ω? (diameter of wire is 0.5mm).

2. Find the resistance of a wire of length 0.65m, radius 0.2mm and resistivity 3 x 10^-6ohm-meter.

3. If a current of 0.75A is generated when a battery of 1.5 V is connected to a 5m wire having cross sectional area 2.5 × 10^-7 m², what will be the resistivity?

3. OHM'S LAW AND SIMPLE DC CIRCUIT ANALYSIS

Ohm’s law gives the relationship between voltage, current and resistance in a simple DC circuit. V = IR. Equivalent, . In addition, this implies that current is directly proportional to voltage if resistance is constant and also current is inversely to resistance is voltage remains constant.

Simple DC circuit

In direct current (DC) circuits, the voltage, source (Battery, power supply) maintains a constant polarity and magnitude of voltage. We assume the circuit is made of resistors an wires with negligible resistance.

Common DC configuration

Series connection

In a series connection, resistors are connected end to end, so that the current flows through each resistor in turn. The total resistance of the series connection is equal to the sum of the individual resistances of the resistors. The current through each resistor in a series connection is the same, and the voltage across the series connection is divided among the resistors in proportion to their resistance.

Let three resistors R₁, R₂ and R₃as shown below

Let V= Voltage applied across the series combination

I = Current passing through the circuit

Clearly current I is same throughout the circuit

Let V₁, V₂, V₃ be the potential difference across R₁, R₂, R₃ respectively. Then, according to Ohm’s law

V = I R

where R is the total resistance in series

Now

V = V₁ + V₂ + V₃--------------- (1)

Then by Ohm’s law

V₁ = I R₁

V₂ = I R₂

V₃ = I R₃

Putting the values of V₁, V₂ and V₃ in equation (1) we get

IR = I R₁+I R₂+I R₃

IR = I (R₁+R₂+ R₃)

R = (R₁+R₂+ R₃)

Thus, the combined resistances when they are connected in series is the sum total of the individual resistances.

Characteristics of Resistors in series

Same current: The same electric current flows through every resistor because there is only one path for current.
Total resistance increases: The total resistance is the sum of all the individual resistances.
Voltage is shared: The supply voltage is divided among the resistors. The voltage drops across each resistor depends on its resistance.
Higher resistance gets a higher voltage drop: If the same current flows through different resistors, the resistor with the greatest resistance has the greatest voltage drop, according to Ohm’s law.
Failure of one resistor breaks the circuit: If one resistor becomes open-circuit, current stops flowing through all the resistors.
Equivalent resistance is greater than any individual resistance: For positive resistance values, the total resistance is greater than each individual resistor.
Current decreases when more resistance is added: If the supply voltage remains constant, adding another resistor in series increases the total resistance and reduces the current.

Parallel connection

In a parallel connection, resistors are connected across each other, so that the voltage across each resistor is the same. The total resistance of the parallel connection is less than the smallest individual resistance of the resistors. The current through each resistor in a parallel connection is divided among the resistors in proportion to their resistance.

Let there be three resistors R₁, R₂, R₃ connected in parallel as shown in Figure 3.2. One end of each resistance is connected to point A and the other end of each resistance is connected to the point B.

Let V = Potential Difference applied across A and B clearly, potential difference V is same across each resistance.

Let I = total current flowing in the circuit.

R = total resistance of the circuit

Let I₁, I₂, I₃ be the current passing through the resistances R₁, R₂, R₃ respectively. From Ohm’s law applied to the whole circuit.

Now we have,

I = I₁+ I₂+ I₃ -----------------------(2)

Putting the values of I, I₁, I₂, I ₃ in the equation (2)

Thus, we can say that if the resistors are connected in parallel, then the reciprocal of the equivalent resistance is equal to the sum of reciprocals of individual resistances in the circuit.

Characteristics of Resistors in Parallel

Same voltage: The voltage across each resistor is equal to the supply voltage
Current is divided: The total current divides among the different branches. The amount flowing through each resistor depends on its resistance.
Total resistance decreases: The reciprocal of the total resistance equals the sum of the reciprocals of the individual resistances.
Total resistance is less than the smallest resistor: Adding more parallel resistors provides additional paths for current, reducing the equivalent resistance.
Failure of one branch does not necessarily stop the others: If one resistor becomes open-circuit, current can still flow through the other parallel branches.
Adding more resistor increases total current: When the supply voltage remains constant, adding another parallel resistor decreases the total resistance and increases the total current drawn from the supply
A lower resistance carries more current: For the same voltage across each branch, a resistor with lower resistance carries a greater current, according to Ohm’s law.

Examples

1) Calculate the total resistance when resistors of 2Ω and 3Ω are connected in parallel.

2) Calculate the total resistance when three resistors of 4Ω, 8Ω, and 14Ω are connected in series.

3) Three resistors 1Ω, 2Ω and 3Ω are combined in series.

a) What is the total resistance of the combination?

b) If the combination is connected to a battery of emf 12V and negligible internal resistance, obtain the potential drop across each resistor.

4. A wire 4.0 m long and 6.00 mm diameter has a resistance of 15.0 Wm. A potential difference of 23.0V is applied between the ends of the wire,

(a) what is the current through the wire.

(b) calculate the resistivity of the wire material.

Energy Dissipation and Power in electrical Circuit

Energy and power in electrical circuit describe how electrical energy is converted into heat or other forms per unit time when electric current flows through a device, especially resistor

Electrical Power

Power (P) is defined as the rate of doing work. Power is measured in watts (W).

Power = work done/time taken

Electric power is the amount of electrical work done per second.

from W = IVt

P = IVt/t = IV = R

Energy dissipation in resistors

when current flows through a resistor, electrical potential energy is lost athe charges move through the material. This energy is dissipated as heat. The power dissipated in resistor R carrying current I, is given by; P = R. If the resistor has a fixed voltage V applied across it. P = . This is because resistors are never perfect, this power dissipation causes the components to heat up. The maximum safe power a resistor can handle without burning is call its power rating e.g. 0.5wtt, 1wtt etc.

Total Dissipated Energy Over Time

If a device dissipates power P for a time t, the total energy E lost (Mainly as heat) is calculated as E = Pt

Using the different forms of power, this becomes

E = VIt = Rt =

4.3.1 Examples

1. Calculate the current in a 60W light bulb when it is connected to a 230V power supply.

2. A large power station supplies electrical energy to the grid at a voltage of 25kV. Calculate the output power of the station when the current it supplies is 40kA

3. A 12V car battery can supply a current of 10A for 5.0 hours. Calculate how many joules of energy the battery transfers in this time.

4. A lamp is operated for 20s. The current in the lamp is 10A. In this time, it transfers 400J of energy to the lamp. Calculate:

a. how much charge flows through the lamp

b. how much energy each coulomb of charge transfers to the lamp

c. the p.d. across the lamp.

A small electronic device is rated at 0.25 W when connected to 120 V. What is the resistance of this device?

A calculator is rated at 0.10 W and has an internal resistance of 22 Ω. What battery potential difference is required for this device?

4. ENERGY DISSIPITATION IN RESISTORS