Current, voltage, and resistance are connected by a simple equation. Ohm’s law is one of the important laws in middle-school physics.
Basic Knowledge
Ohm’s law: Voltage V [V] is equal to the product of current I [A] and resistance R [Ω].V = IR
Rearranging the equation:
・To find current: I = V / R
・To find resistance: R = V / I
Electrical resistance R represents how difficult it is for current to flow, and its unit is the ohm (Ω).
Resistor connections:
・Equivalent resistance of a series connection: R = R₁ + R₂ (sum)
・Equivalent resistance of a parallel connection: 1/R = 1/R₁ + 1/R₂ (sum of reciprocals)
When resistors are connected in parallel, the equivalent resistance becomes even smaller than the smallest resistance.
Ohm’s law (V = IR)
Electrical resistance R (difficulty of current flow. Unit: Ω (ohm))
Conductor (a substance that conducts electricity easily. Metals, copper, aluminum)
Nonconductor (insulator) (a substance that does not conduct electricity easily. Rubber, plastic, wood)
Semiconductor (a substance that can act as either a conductor or an insulator depending on conditions. Silicon, germanium)
Equivalent resistance (the resistance value obtained by combining multiple resistors into one)
Further Exploration (Background and Significance)
Ohm announced this law in 1827. Collisions between flowing electrons and ions inside metals create resistance.
Resistance changes even when the material is the same:
・The longer a wire is, the greater its resistance; the shorter it is, the smaller its resistance
・The thicker a wire is, the smaller its resistance; the thinner it is, the greater its resistance
This can be expressed as “inversely proportional to cross-sectional area and proportional to length.”
Examples of resistance values: 0.017Ω for 1m of copper wire, about 100Ω for an incandescent light bulb, several thousand to several tens of thousands of Ω for a dry human body, and about 1000Ω for wet skin.
Semiconductors are the foundation of computers, and their resistance can be finely controlled by the amount of impurities. Transistors and integrated circuits made using silicon are among the greatest inventions of the latter half of the 20th century.
- Ohm’s law: V = IR
- Unit of resistance R: Ω (ohm)
- Classification into conductors, insulators, and semiconductors
- Series equivalent: R = R₁ + R₂
- Parallel equivalent: 1/R = 1/R₁ + 1/R₂
- The longer a wire, the greater its resistance; the thicker it is, the smaller its resistance
- Semiconductors are the foundation of computers and electronic devices
Points to Note (Easily Confused)
① The unit of resistance is Ω (ohm). It differs from the unit of voltage, V. ② The equivalent resistance in parallel is the reciprocal of the sum of the reciprocals. It is not a “simple sum.” ③ Parallel connection makes the equivalent resistance smaller (because it increases the paths through which electricity can flow). ④ Ohm’s law is exact only when resistance is constant. If resistance changes because of heating, as in a light bulb, the relationship becomes curved.
Practice
- Find the voltage when a current of 3A flows through a 20Ω resistor.
- When a 4Ω resistor is connected to a 12V power source, what current flows?
- Find the equivalent resistance when 10Ω and 15Ω resistors are connected in series.