Resistance
Resistance definition: Resistance is a way to describe how much a material tries to stop electricity from flowing through it. If a material has high resistance, it is harder for electric current to pass through. If it has low resistance, the current can flow easily.
Charge hindrance: When we say a component resists the movement of electrons, it means that it slows down or blocks the tiny particles (electrons) that carry electricity. This slowing down is what we call resistance.
Resistance formula: To find the resistance of something, we use the formula R = V/I. This means resistance (R) is equal to the voltage (V) across the component divided by the current (I) flowing through it. It’s like figuring out how hard it is for electricity to move.
Resistance unit: The unit used to measure resistance is called the ohm. Its symbol is the Greek letter omega (Ω). If something has a resistance of 1 ohm, it means that 1 volt of electricity will produce a current of 1 ampere.
Friction analogy: Resistance is like friction in a pipe of water. Just like rough pipes make water harder to flow, high resistance makes electricity harder to move. Lower resistance is like smooth pipes—it lets the current move easily.
Ohm's Law
Law statement: Ohm’s Law tells us that if we keep the temperature and other physical conditions the same, then the amount of electric current going through a conductor increases when we increase the voltage. This means current and voltage go up and down together.
Ohm’s Law equation: We write Ohm’s Law as V = IR. This formula shows the link between voltage (V), current (I), and resistance (R). It helps us figure out any one of them if we know the other two.
Ohmic conductors: Some materials follow Ohm’s Law exactly. These are called ohmic conductors. When you draw a graph of voltage versus current for them, the line is straight and goes through the origin (0,0). That means they have a constant resistance.
Ohmic examples: A good example of an ohmic conductor is a metal wire like copper when it is kept at the same temperature. The current and voltage increase steadily with each other.
Non-ohmic conductors: Not all materials follow Ohm’s Law. These are called non-ohmic conductors. In these materials, the resistance changes as the current or voltage changes. Their graphs are not straight lines.
Non-ohmic examples: Devices like filament lamps, thermistors (used in temperature sensing), and diodes (used in circuits to control direction of current) are examples of non-ohmic conductors.
Graph explanation: On a voltage-current (V-I) graph, the slope or gradient of the line shows the resistance. A straight line means the resistance is steady (ohmic). A curved line means the resistance changes (non-ohmic).
Factors Affecting Resistance
Length effect: When we talk about how the length of a wire affects resistance, we mean that the longer the wire is, the more resistance it creates. In physics, we write this relationship as R ∝ l, which means resistance (R) is directly proportional to the length (l) of the wire. So, if you double the length of the wire, the resistance will also double.
Explanation of length: This happens because as electricity flows through a wire, the tiny particles called electrons have to move along the entire length of the wire. In a long wire, the electrons must travel a longer distance and along the way, they bump into more atoms inside the wire. These collisions slow the electrons down, making it harder for the electric current to pass through. That’s why longer wires have more resistance.
Area effect: If the wire is thicker (has a larger cross-sectional area), it has less resistance. This is shown by the formula R ∝ 1/A, which means resistance is inversely proportional to area. So, as the area increases, resistance decreases.
Explanation of area: A thicker wire gives the electrons more space to move around. With more room, the electrons bump into fewer atoms, which means they can move more easily. It’s just like walking through a wide hallway instead of a narrow one—you can move faster and easier in the wide hallway. That’s why thicker wires have less resistance.
Resistivity definition: Resistivity is a special property of a material. It tells us how much that material naturally resists the flow of electric current. Every type of material has its own resistivity, and it doesn’t change based on the size or shape of the material—it’s just a built-in property of what the material is made of.
Material types: Some materials like rubber have high resistivity, which means they don’t let electric current pass through easily. That’s why rubber is used as an insulator. On the other hand, materials like copper have low resistivity, meaning electric current can pass through them easily. That’s why copper is used to make wires and conductors.
Resistivity unit: Resistivity is measured using a unit called the ohm-metre (Ωm). This unit combines the idea of resistance (how hard it is for current to flow) and the length of the wire. It helps engineers and scientists compare materials more easily.
Temperature effect on metals: When the temperature of most metals goes up, their resistance also goes up. This is because higher temperatures make the atoms inside the metal move or vibrate more. When the atoms vibrate more, they get in the way of the electrons trying to move through the wire, which causes more collisions and makes it harder for electricity to flow.
Temperature effect on semiconductors: In semiconductors, the opposite usually happens. As the temperature goes up, their resistance goes down. This is because higher temperatures release more electrons that can move freely and carry electric current. So, the material becomes better at conducting electricity when it’s hotter.
Combined resistance formula: All the factors we’ve talked about—resistivity, length, and area—can be combined into one single formula: R = ρl/A. In this formula, R is resistance, ρ (rho) is resistivity, l is the length of the wire, and A is the cross-sectional area. This formula helps us understand how resistance changes depending on what the wire is made of, how long it is, and how thick it is.
Resistors in Series
Series definition: A series circuit is when we connect electrical parts (like bulbs or resistors) one after another in a straight line. In this kind of circuit, there is only one single path for the current to travel through.
Current in series: Because there is only one path, the same electric current flows through every resistor in a series circuit. The amount of current is the same at every point in the circuit.
Total resistance in series: To find the total resistance in a series circuit, we simply add up all the resistances of each resistor. This is written as: R = R₁ + R₂ + R₃ + …. The more resistors you add, the bigger the total resistance becomes.
Voltage in series: The total voltage (or energy) provided by the battery or power supply is shared among the resistors in a series circuit. This means V = V₁ + V₂ + V₃ + …, where the voltage is divided between the parts.
Resistors in Parallel
Parallel definition: A parallel circuit is when components are connected so that there are multiple paths for the current to flow. All the components are connected across the same two points.
Voltage in parallel: In a parallel circuit, each resistor is connected directly across the battery or power source. That means each resistor gets the same voltage.
Current in parallel: The total current in a parallel circuit is divided among the different branches. That means the total current I = I₁ + I₂ + I₃ + …, where each branch gets part of the total current.
Total resistance in parallel: In a parallel circuit, the total resistance is less than the resistance of any one of the individual resistors. To find the total resistance, we use the formula: 1/R = 1/R₁ + 1/R₂ + 1/R₃ + …. This usually gives a smaller total resistance than the smallest resistor in the group.
Key Differences Between Series and Parallel Circuits
Current flow: In a series circuit, the current is the same everywhere—it flows through each component one after another. In a parallel circuit, the current splits up and flows through different branches.
Voltage distribution: In a series circuit, the total voltage is shared among all the components. In a parallel circuit, each component gets the full voltage from the battery.
Resistance behavior: In a series circuit, the resistances add up directly. In a parallel circuit, we use a special formula with reciprocals to calculate total resistance. This usually gives a total resistance that is smaller than any one resistor on its own.