Ohm’s law and electrical power explain how electric circuits behave when charges move through wires, bulbs, resistors, and devices. This cheat sheet helps students connect voltage, current, resistance, power, and energy using the formulas most often needed in middle and high school physics. It is useful for solving circuit problems, checking units, and understanding how electrical devices use energy.
Key Facts
- Ohm’s law is , where is voltage in volts, is current in amperes, and is resistance in ohms.
- Current can be found from Ohm’s law using .
- Resistance can be found from Ohm’s law using .
- Electrical power is , where is power in watts, is voltage, and is current.
- Using Ohm’s law with power gives and .
- Electrical energy is , where is energy, is power, and is time.
- In a series circuit, current is the same through each component and total resistance is .
- In a parallel circuit, voltage is the same across each branch and total resistance follows .
Vocabulary
- Voltage
- Voltage is the electric potential difference that pushes charge through a circuit, measured in volts.
- Current
- Current is the rate at which electric charge flows through a circuit, measured in amperes.
- Resistance
- Resistance is how much a material or component opposes the flow of electric current, measured in ohms.
- Ohm’s Law
- Ohm’s law states that voltage equals current times resistance, written as .
- Electrical Power
- Electrical power is the rate at which electrical energy is transferred or used, measured in watts.
- Electrical Energy
- Electrical energy is the amount of energy transferred by a circuit over time, often found using .
Common Mistakes to Avoid
- Mixing up current and voltage is wrong because current is charge flow while voltage is the energy push per charge.
- Using with resistance instead of current is wrong because must be in amperes; use or when resistance is given.
- Forgetting to convert units is wrong because time in must match the energy unit, such as seconds for joules or hours for kilowatt-hours.
- Adding resistors in parallel like series is wrong because parallel resistance must use .
- Assuming higher resistance always means higher power is wrong because power depends on the circuit conditions and may follow or .
Practice Questions
- 1 A resistor has and current . Find the voltage across the resistor.
- 2 A lamp uses when connected to . Find the current through the lamp.
- 3 A device runs at for . Find the electrical energy used in kilowatt-hours.
- 4 Two bulbs are connected to the same battery, but one has a much larger resistance. Explain which bulb has less current and why.
Understanding Ohm's Law & Electrical Power
Voltage is best understood as an energy difference between two places in a circuit. A cell, battery, or power supply separates charge and creates this difference. When a complete conducting path exists, charge begins to move.
Conventional current is defined as moving from the positive terminal toward the negative terminal. In metal wires, the mobile electrons actually move in the opposite direction. Both descriptions can be used correctly if the chosen direction stays consistent.
Current is not used up as it travels around a simple series circuit. The charges carry energy from the source, then transfer some of it to components such as lamps, heaters, or motors.
Resistance comes from collisions inside a material. Moving electrons collide with atoms, impurities, and defects in the material. These collisions make charge flow harder and can warm the component.
A long thin wire has more resistance than a short thick wire made from the same material. Different materials matter too. Copper has low resistance, so it is useful for household wiring.
The thin metal filament in an old-style lamp has much higher resistance, so it gets hot enough to glow. Temperature can change resistance. For many metal conductors, resistance rises as temperature rises, which affects real measurements.
Series and parallel circuits behave differently because they offer different paths for charge. In a series arrangement, every charge must pass through each component in turn. Adding another resistor makes the path harder overall, so the current from a fixed supply falls.
In a parallel arrangement, each branch connects across the same supply. More branches provide more routes for charge, so the total current drawn from the source can rise. This is why homes use parallel wiring.
Turning off one lamp does not stop current in the other branches. A short circuit is dangerous because it creates a very low resistance path, allowing a very large current that can overheat wires.
Power tells how quickly a device transfers electrical energy. A higher power kettle heats water faster than a lower power kettle when both work normally, but it uses energy more quickly. Energy use depends on power and running time.
A device rated at one thousand watts uses one kilowatt of power. If it runs for one hour, it uses one kilowatt-hour of energy. Electricity bills commonly use kilowatt-hours, not joules.
When solving problems, first identify what remains the same in the circuit. Current stays the same in a series path, while voltage stays the same across parallel branches. Check units carefully and make sure power is in watts, energy is in joules or kilowatt-hours, and time matches the energy unit being used.