# Resistance and Ohm's Law

## Ohm's Law

In 1827, George Ohm demonstrated through a series of experiments that voltage, current, and resistance are related through a fundamental relationship: Voltage (V) is equal to Current (I) times resistance (R), or $V = I\cdot R$. This most basic equation in electronics shows that when any two of the three quantities are known, the third can be derived. The Ohm's law triangle in Fig. 1 below shows how to derive each variable given the other two. An important thing to note about Ohm's law is that a resistor's voltage and current are related by its resistance.

## Resistance

Resistance is measured in ohms, represented by the symbol Omega (Ω). According to Ohm's law, one volt impressed across 1 ohm of resistance will cause 1 amp of current to flow. Similarly, 3.3V impressed across 3.3Ω will cause 1A of current to flow. In Fig. 2, the lines leaving the positive and negative sides of the power supply represent conductors with an insignificant amount of resistance. Thus, the voltage delivered by the power supply is present at both sides of the resistor - 3.3V at the left side of the resistor, and 0V (GND) and the right side of the resistor. As current flows through the resistor, collisions occur between the electrons flowing from the power supply and the materials in the resistor. These collisions cause electrons to give up their potential energy, and that energy is dissipated as heat. As with any physical system, we define the time derivative of energy as power; in electric circuits, power (measured in Watts) is defined as voltage times current, or $P = V\cdot I$. The power transferred to the resistor at any given time results in resistor heating. The more power transferred to the resistor, the hotter it gets. For a given voltage, a smaller-valued resistor would allow more current to flow (see Ohm's law), and therefore more energy would be dissipated as heat. The total energy consumed in an electric circuit is simply the time integral of power, measured in Watts per second, or Joules. Thus, in the circuit above, the electric power delivered to the resistor is $P = 3.3V \times 1A$, or 3.3Watts, and in one second, $3.3W \times 1second$ or 3.3J of energy is dissipated. Many devices can provide only limited current; if your circuit draws too much current from the device, it can malfunction. Increasing the resistance in your circuit may solve this problem.

## Important Ideas

• Resistance is measured in Ohm's (Ω).
• Ohm's law states that 1 volt impressed upon 1 ohm of resistance will cause 1 amp of current to flow.
• In circuits, power is measured in Watts, which is measured in voltage times current.
• The power of an electric circuit is measured in Watts, or Joules per Second.