Current Electricity fundamentally deals with the controlled flow of electric charge through a conductor. This flow, termed electric current, is defined as the rate of flow of charge and is measured in Amperes. For a current to exist steadily, a source like a cell or battery is essential. It establishes a potential difference (voltage) across the ends of a conductor, which is the work done to move a unit charge and acts as the driving force that pushes the charges. The relationship between this potential difference, the current flowing, and the inherent opposition offered by the conductor (resistance) is precisely given by Ohm’s Law. This law states that at constant physical conditions like temperature, the current through a conductor is directly proportional to the potential difference across its ends.
Resistance, measured in Ohms, is a property that depends on the material, length, cross-sectional area, and temperature of the conductor. While conductors like metals offer low resistance, components called resistors are specifically used in circuits to introduce a desired amount of resistance. The effective resistance of combinations of resistors can be calculated differently for series and parallel arrangements. In a series combination, the total resistance is simply the sum of individual resistances, and the same current flows through each resistor. In contrast, in a parallel combination, the reciprocal of the total resistance equals the sum of reciprocals of individual resistances, and the potential difference remains the same across each branch.
Moving beyond basic principles, the chapter also covers practical electrical concepts like electrical power and energy. Electrical power is the rate at which electrical energy is consumed or converted into other forms like heat or light, and is calculated as the product of potential difference and current. Its unit is the Watt. Electrical energy, which is the total work done or power consumed over time, is commercially measured in kilowatt-hours (kWh). Furthermore, the heating effect of electric current is explained by Joule’s Law, which states that the heat produced is directly proportional to the square of the current, the resistance, and the time for which it flows. This effect finds applications in everyday devices such as electric heaters, bulbs, and fuses, where the purpose of a fuse is to protect circuits by melting and breaking the connection when the current exceeds a safe limit.
Question 1:
Define the term current and state its S.I unit.
Ans:
Electric current measures how quickly electric charge moves through a specific part of an electrical circuit. In essence, it quantifies the amount of charge that travels past a given point within a certain timeframe.
The standard unit for measuring this flow in the International System of Units is the ampere, denoted by the letter A. By definition, a current of one ampere is equivalent to the transfer of one coulomb of electrical charge each second.
Question 2:
Define the term electric potential. State its S.I. unit.
Ans:
Electric potential refers to the amount of work required to move a unit positive charge from a reference point—typically taken as infinity—to a specific point within an electric field, without causing any acceleration. It essentially represents the electric potential energy per unit charge at that point. The S.I. unit for electric potential is the volt, denoted by V. One volt is equivalent to one joule per coulomb.
Question 3 :
How is the electric potential difference between the two points defined? State its S.I. unit.
Ans:
The electric potential difference between two points in a circuit is defined as the amount of work done in moving a unit positive charge from one point to the other against the electric field. In simpler terms, it represents the difference in electrical potential energy per unit charge at the two points. This difference is what causes electric charges to flow if a path is provided, as charges naturally move from a point of higher potential to a point of lower potential.
The SI unit of electric potential difference is the volt, denoted by the symbol V. One volt is equivalent to one joule of work done in moving one coulomb of charge between the two points. Therefore, 1 V = 1 J/C. A common analogy is to think of it like water pressure in a pipe; just as a difference in water pressure causes water to flow, a potential difference (voltage) causes electric current to flow in a conductor.
Question 4:
Explain the statement ‘the potential difference between two points is 1 volt’.
Ans:
The statement ‘the potential difference between two points is 1 volt’ is a precise way of defining the electrical ‘push’ or pressure between those points. Fundamentally, electric potential is a measure of the electrical potential energy stored per unit charge at a point. Therefore, a potential difference of 1 volt specifically means that for every 1 coulomb of electric charge that moves between those two points, 1 joule of work is done by the electric forces, or equivalently, 1 joule of electrical energy is converted into another form, such as heat or light.
A helpful way to visualize this is to compare it to gravity. Imagine two different heights; water will naturally flow from the higher point to the lower one, releasing energy. Similarly, in an electrical circuit, charge flows from a point of higher electrical potential (like the positive terminal of a battery) to a point of lower potential (the negative terminal). The volt is the unit that measures this ‘electrical height’ difference. A 1.5-volt battery has a smaller potential difference—or a gentler ‘electrical slope’—than a 9-volt battery, meaning it does less work on each unit of charge that moves through it.
In practical terms, when you connect these two points with a conductor, this 1-volt potential difference is the driving force that causes an electric current to flow. It tells us the energy cost of moving charge. If you have to do 1 joule of work to move 1 coulomb of charge against the electric field from the lower to the higher potential point, then the potential difference you are working against is exactly 1 volt. This standardized measurement allows us to calculate the energy transferred in any circuit, as the total energy (in joules) is simply the product of the potential difference (in volts) and the total charge that flows (in coulombs).
Question 5:
Explain the analogy between the flow of charge (or current) in a conductor under a potential difference with the free fall of a body under gravity.
Ans:
The movement of charge through a conductor and the free fall of a body under gravity share a foundational similarity rooted in the concept of potential-driven motion. This analogy helps illustrate how energy differences propel objects or particles from one state to another. Below, we explore this parallel step by step, focusing on the core principles that link these two phenomena.
In free fall under gravity, a body released from a height descends toward the ground due to the gravitational force. This force arises from the difference in gravitational potential—essentially, the body moves from a point of higher potential energy to one of lower potential energy. As it falls, its potential energy decreases while its kinetic energy increases, assuming negligible air resistance. The acceleration remains constant (approximately 9.8 m/s² on Earth), meaning the velocity increases linearly with time. The driving factor here is the gravitational potential difference, often conceptualized as the height from which the body falls; a greater height implies a larger potential difference and thus a higher final velocity upon impact.
In the case of charge flow in a conductor, a similar dynamic occurs. When a potential difference (voltage) is applied across the ends of a conductor, an electric field is established within it. This field exerts a force on free charges (like electrons), pushing them from a region of higher electric potential to lower electric potential. Just as gravity pulls a mass downward, the electric field accelerates charges along the conductor. However, in a realistic conductor, charges do not accelerate indefinitely; they frequently collide with atoms in the material, losing energy and momentum. These collisions result in a net average motion known as drift velocity, which remains constant for a given electric field. The current, defined as the rate of charge flow, is thus steady under a constant potential difference.
The analogy becomes clear when we map corresponding elements. The gravitational potential difference (height) mirrors the electric potential difference (voltage). The mass of a body in gravitational systems parallels the charge in electrical systems—both represent the “quantity” that experiences the force. The gravitational force (weight) is analogous to the electric force on charges. Additionally, the constant acceleration in free fall corresponds to the initial acceleration of charges between collisions in a conductor, though the latter is interrupted by resistive interactions.
Energy transformation offers another point of comparison. In free fall, potential energy converts to kinetic energy continuously. In a conductor, electrical potential energy converts into kinetic energy of charges, but this energy is quickly dissipated as heat due to collisions, akin to how air resistance would dissipate energy in a non-ideal fall. This dissipation highlights a key difference: free fall in a vacuum is lossless, while charge flow inherently involves resistance. Nonetheless, the core idea persists—motion is driven by a drop in potential.
This analogy aids in visualizing why current flows only when there is a potential difference, much like a body falls only when there is a height difference. It also underscores the directional nature of both processes: from high potential to low potential. However, it is crucial to recognize the limits of the analogy. For instance, in free fall, velocity increases unabated without resistance, whereas in conductors, drift velocity stabilizes quickly due to internal collisions. Despite this, the analogy remains a valuable tool for intuitive understanding, bridging familiar gravitational concepts with the less tangible flow of electricity.
Question 6:
Define the term resistance. State its S.I. unit.
Ans:
Resistance is an inherent characteristic of any material that hinders the movement of electric charge. This opposition originates as free electrons drift through the conductor, repeatedly colliding with the relatively stationary ions in its atomic structure. These interactions convert some electrical energy into heat. The magnitude of this impediment is quantified in the unit called the ohm, denoted by the symbol Ω.
Question 7:
Name the particles which are responsible for the flow of current in a metal. Explain the flow of current in a metal on the basis of movement of the particles name by you.
Ans:
The particles responsible for the flow of electric current in a metal are free electrons. These electrons are not bound to individual atoms but are able to move freely throughout the metallic lattice.
Explanation of Current Flow Based on Electron Movement:
These free electrons move randomly in all directions at high speeds due to thermal energy, but there is no net directional flow without an external influence.
When a voltage is applied across the ends of a metal conductor, it creates an electric field along the conductor. This electric field exerts a force on the free electrons, accelerating them in a direction opposite to the field (since electrons are negatively charged). However, electrons frequently collide with ions in the lattice, which deflects them and transfers energy, causing resistance. Despite these collisions, the electric field imposes a net drift velocity on the electrons, causing them to drift slowly in the opposite direction to the electric field.
This coordinated drift of free electrons constitutes an electric current. The magnitude of the current is determined by the rate at which charge flows through a cross-section of the conductor. Importantly, while individual electrons move slowly due to collisions, the electric field propagates nearly at the speed of light, so current appears to start almost instantly when voltage is applied.
Conventional current direction is defined as the flow of positive charge from the higher potential to the lower potential. In reality, electrons flow from the lower potential to the higher potential, but the effect is equivalent to positive charge flowing in the opposite direction. Thus, the flow of current in metals is essentially due to the drift of free electrons under the influence of an electric field.
Question 8:
How does the resistance of a wire depend on its radius? Explain your answer.
Ans:
Since the cross-sectional area of a cylindrical wire is circular, it is calculated using the formula A = πr², where ‘r’ is the radius. This means the area is directly proportional to the square of the radius (A ∝ r²).
Therefore, resistance (R) is inversely proportional to the square of the radius (R ∝ 1/r²). This relationship shows that the radius has a very strong effect on resistance. For example, if the radius of a wire is doubled, its cross-sectional area becomes four times larger. Consequently, the resistance decreases to one-fourth of its original value, assuming the length and material of the wire remain unchanged.
In practical terms, this explains why thicker wires (with a larger radius) offer much less opposition to the flow of electric current. They are used in applications requiring high currents, such as in main power supply cables, to minimize energy loss due to heating. Conversely, thinner wires, with their smaller radius and greater resistance, are suitable for components where current needs to be limited.
Question 9:
How does the resistance of a wire depend on its length? Give a reason for your answer with reason.
Ans:
The resistance of a wire increases directly with its length. This means that if you take a wire and make it longer, its resistance will rise proportionally. For example, doubling the length of the wire will double its resistance, provided all other conditions stay the same.
The reason for this lies in how electric current flows through the wire. Current consists of electrons moving through the material. As these electrons travel, they bump into atoms and other imperfections in the wire’s structure, which slows them down. This hindrance to electron flow is what we call resistance. In a longer wire, electrons must pass through more atoms and obstacles along the path, leading to more frequent collisions. As a result, the overall opposition to current—the resistance—becomes greater with increased length. Essentially, a longer wire offers more “roadblocks” to electron movement, making it harder for current to pass through.
Question 10:
How does the resistance of a metallic wire depend on its temperature? Explain with reason.
Ans:
This direct relationship occurs due to the internal atomic structure of metals.
Metals possess a lattice of positive ions surrounded by a “sea” of free electrons, which are the charge carriers. As the temperature of the wire increases, the ions within the lattice gain kinetic energy and vibrate more vigorously and with greater amplitude around their fixed positions. This intensified vibration creates a more crowded and obstructed path for the free electrons trying to drift through the wire when a potential difference is applied. The electrons collide more frequently with these vibrating ions, impeding their orderly flow. Since resistance is essentially a measure of the opposition to the flow of current, these increased collisions result in a higher overall resistance.
This behavior is quantitatively expressed by the formula: Rₜ = R₀[1 + α(T – T₀)], where Rₜ is the resistance at temperature T, R₀ is the resistance at a reference temperature T₀, and α is the temperature coefficient of resistance, which is positive for pure metals. This principle is utilized in devices like resistance thermometers, where the measurable change in resistance is used to accurately calculate temperature changes.
Question 11:
Two wires, one of copper and other of iron, are of the same length and same radius. Which will have more resistance? Give a reason.
Ans:
Resistance depends not only on a wire’s physical dimensions (length and thickness) but also on the intrinsic property of the material itself, known as resistivity. Each material has a specific resistivity value at a given temperature. Iron has a significantly higher resistivity than copper. Since both wires are identical in length and cross-sectional area, the only differing factor is the material. According to the formula for resistance, R = ρL/A (where ρ is resistivity, L is length, and A is area), the wire with the higher resistivity (iron) will inevitably have the higher resistance.
Therefore, when comparing two wires of identical size, the one made from a material with greater resistivity will always offer more opposition to current flow. In this case, the iron wire’s higher natural opposition to electric charge movement makes it more resistive than the copper wire.
Question 12:
Name three factors on which resistance of a given wire depends and state how it is affected by the factors stated by you.
Ans:
The resistance of a given wire is influenced by three primary factors:
- Length of the wire: The resistance is directly proportional to the length of the wire. When the wire is longer, the electrons face more obstacles along the path, leading to higher resistance. Conversely, shortening the wire reduces the resistance.
- Cross-sectional area of the wire: A thicker wire with a larger area offers more space for electrons to flow, decreasing resistance. On the other hand, a thinner wire with a smaller area restricts electron flow, increasing resistance.
- Temperature of the wire: For most metallic wires, resistance increases with temperature. As temperature rises, atomic vibrations within the wire intensify, causing more collisions that hinder electron movement. Lowering the temperature reduces these vibrations, thereby decreasing resistance.
