Electricity Revision Notes

Ohm's Law and its Application

Ohm's Law describes the relationship between voltage (V), current (I), and resistance (R): V = I × R. This fundamental law is used to calculate one of these quantities if the other two are known. For example, if you know the voltage across a component and the current flowing through it, you can calculate its resistance (R = V/I). Similarly, if you know the resistance and the voltage, you can find the current (I = V/R). Remember, voltage is measured in volts (V), current in amperes (A), and resistance in ohms (Ω). This relationship is crucial for understanding how electrical components behave in a circuit and for solving simple circuit problems.

Ohmic vs. Non-Ohmic Resistors

Resistors can be classified into two main types based on their behaviour regarding Ohm's Law. An 'ohmic resistor' has a constant resistance, meaning its resistance does not change with varying voltage or current, provided its temperature remains constant. Components like a fixed resistor made of a metal wire often behave ohmically. If you plot a graph of current against voltage for an ohmic resistor, you will get a straight line passing through the origin. In contrast, 'non-ohmic resistors' (or non-ohmic conductors) have a resistance that changes with current or voltage. Examples include filament lamps, diodes, and thermistors. Their current-voltage graphs are not straight lines. For a filament lamp, resistance increases as the current increases due to heating effects.

PAG: Investigating Resistance

A common practical activity (PAG P6) involves investigating the resistance of different components. This can be done by setting up a circuit containing a power supply, an ammeter (in series), a voltmeter (in parallel across the component), and the component itself (e.g., a resistor, a filament lamp). The independent variable is the voltage across the component (controlled by a variable power supply or by varying the number of cells). The dependent variable is the current flowing through the component. Control variables include the temperature of the surroundings. By taking several readings of voltage and current, you can calculate the resistance for each point (R = V/I) and plot a V-I graph. For an ohmic resistor, the graph will be a straight line through the origin, indicating constant resistance. For a filament lamp, the graph will curve, indicating that resistance increases as the current increases.

Series Circuits Explained

In a series circuit, components are connected end-to-end, creating a single path for the electric current. This has several important consequences: the current (I) is the same through every component in the circuit. If one component fails, the entire circuit is broken, and no current will flow. The total potential difference (V_total) across the circuit is the sum of the potential differences across each individual component (V_total = V1 + V2 + V3 + ...). This distribution of voltage is a key characteristic of series connections.

Calculating Equivalent Resistance in Series

When resistors are connected in series, their individual resistances add up to give the total or equivalent resistance (R_total). The formula for calculating this is: R_total = R1 + R2 + R3 + ... where R1, R2, R3, etc., are the resistances of the individual resistors. This means that adding more resistors in series will always increase the total resistance of the circuit. This higher total resistance will lead to a lower total current flowing from the power source, assuming the potential difference remains constant, according to Ohm's Law.

Key Electrical Equations

To solve problems involving series circuits, you need to use the following fundamental equations:

• Ohm's Law: Potential difference (V) = Current (I) × Resistance (R), or V = IR.
• Charge: Quantity of charge (Q) = Current (I) × Time (t), or Q = It. Charge is measured in Coulombs (C).
• Power: Power (P) = Potential difference (V) × Current (I), or P = VI. Other forms include P = I²R and P = V²/R. Power is measured in Watts (W).
• Energy Transferred: Energy (E) = Power (P) × Time (t), or E = Pt. Energy is measured in Joules (J).

Applying Equations to Series Circuit Problems

When solving problems with series circuits, first determine the total (equivalent) resistance of the circuit by adding all individual resistances. Then, use Ohm's Law with the total potential difference and total resistance to find the total current flowing from the power source. Remember, this current is the same through every component in the series circuit. You can then use this current, along with the individual resistances, to find the potential difference across each component. Finally, apply the power, charge, and energy equations as needed, ensuring consistent units (Volts, Amperes, Ohms, Coulombs, Watts, Joules, seconds).

What is Electrical Power?

Electrical power is the rate at which electrical energy is transferred or converted into other forms of energy (like heat, light, or mechanical energy) by an electrical device. The unit for power is the watt (W), which is equivalent to one joule per second (J/s). A higher power rating means the device converts energy more quickly.

Relationship between Power, Potential Difference, and Current

The power transferred by a circuit device is directly proportional to both the potential difference (voltage) across it and the current flowing through it. This relationship is given by the formula: Power (P) = Potential Difference (V) × Current (I). For example, if a device has a large voltage across it, meaning each unit of charge carries a lot of energy, and a large current, meaning many charges flow per second, then a significant amount of energy will be transferred per second (high power).

Calculating Energy Transferred

The total energy transferred (E) by a device depends on its power (P) and the time (t) for which it is operating. The relationship is: Energy Transferred (E) = Power (P) × Time (t). The unit for energy is the joule (J), power is in watts (W), and time must be in seconds (s) for this calculation. This formula helps to understand the total energy usage of appliances over a given period.

Units and Practical Examples

Power is measured in watts (W), potential difference in volts (V), current in amperes (A), and time in seconds (s). Energy transferred is measured in joules (J). For example, a 60 W light bulb transfers 60 joules of electrical energy into light and heat energy every second. If it's on for 10 seconds, it transfers 600 joules of energy (60 W × 10 s = 600 J).

Introduction to the Motor Effect (Higher)

When an electric current flows through a conductor, it generates a magnetic field around the conductor. If this conductor is then placed within an external magnetic field (from a permanent magnet or another electromagnet), the two magnetic fields interact. This interaction results in a force being exerted on the current-carrying conductor. This fundamental principle is known as the motor effect, and it is the basis for how electric motors operate, converting electrical energy into mechanical energy.

Determining Force Direction: Fleming's Left-Hand Rule (Higher)

The direction of the force on the current-carrying conductor is perpendicular to both the direction of the current and the direction of the magnetic field. To determine this direction, Fleming's Left-Hand Rule is used:

• Thumb: Points in the direction of the Force (motion).
• Forefinger: Points in the direction of the magnetic Field (North to South).
• Middle Finger: Points in the direction of the Current (positive to negative). This rule is crucial for predicting how a conductor will move in a magnetic field.

Factors Affecting Force Magnitude (Higher)

The strength of the force exerted on the current-carrying conductor depends on several key factors:

1. Magnetic Field Strength: A stronger magnetic field (B) will produce a greater force.
2. Current Magnitude: A larger current (I) flowing through the conductor will result in a greater force.
3. Length of Conductor: A longer section of the conductor (L) exposed to the magnetic field will experience a greater force.

All these factors are directly proportional to the force. The force is zero if the conductor is placed parallel to the magnetic field lines.