19.1 Ohm's law

Electrical current and resistance are fundamental concepts in understanding how electricity flows and behaves. Current measures the rate of charge flow, while resistance opposes this flow. These principles are crucial for analyzing circuits and designing electrical systems.

Ohm's_Law_0### connects voltage, current, and resistance, forming the basis for circuit analysis. This relationship allows us to calculate unknown values in circuits, predict behavior, and select appropriate components for various applications. Understanding these concepts is essential for working with electrical systems.

Electrical Current and Resistance

Current vs charge over time

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• Current represents the rate of flow of electric charge over time
  • Measured in amperes (A) using the symbol $I$
  • Calculated using the formula $I = \frac{Q}{t}$, where $Q$ is the charge in coulombs (C) and $t$ is the time in seconds (s)
• Charge quantifies the amount of electricity
  • Measured in coulombs (C) using the symbol $Q$
  • One coulomb is equal to the charge of approximately $6.24 \times 10^{18}$ electrons
• Direct current (DC) maintains a constant flow of charge in one direction
  • Commonly found in batteries and solar cells
  • Suitable for low-voltage applications (flashlights, mobile devices)
• Alternating current (AC) exhibits a periodic reversal of charge flow direction
  • Commonly found in power outlets and generators
  • Enables efficient long-distance power transmission (power grids)

Resistance and Ohm's law

• Resistance quantifies the opposition to the flow of electric current in a material
  • Measured in ohms ($\Omega$) using the symbol $R$
  • Depends on the material properties (resistivity) and geometry (length, cross-sectional area)
  • Inversely related to conductivity, which measures a material's ability to allow current flow
• Ohm's law establishes a linear relationship between voltage, current, and resistance
  • Voltage across a conductor is directly proportional to the current flowing through it
  • Resistance acts as a constant of proportionality between voltage and current
  • Mathematically expressed as $V = IR$, where $V$ is the voltage in volts (V), $I$ is the current in amperes (A), and $R$ is the resistance in ohms ($\Omega$)
  • Voltage represents the potential difference between two points in an electrical circuit

Applications of Ohm's law

• Calculating current ($I$) when voltage ($V$) and resistance ($R$) are known
  • Formula: $I = \frac{V}{R}$
  • Example: For a 12 V battery connected to a 4 $\Omega$ resistor, the current is $I = \frac{12V}{4\Omega} = 3A$
• Determining voltage ($V$) when current ($I$) and resistance ($R$) are known
  • Formula: $V = IR$
  • Example: If a 2 A current flows through a 6 $\Omega$ resistor, the voltage across the resistor is $V = 2A \times 6\Omega = 12V$
• Finding resistance ($R$) when voltage ($V$) and current ($I$) are known
  • Formula: $R = \frac{V}{I}$
  • Example: If a 9 V battery causes a 1.5 A current to flow, the resistance of the circuit is $R = \frac{9V}{1.5A} = 6\Omega$
• Ohm's law is essential for analyzing and designing electrical circuits
  • Helps determine the required voltage, current, or resistance for a specific application
  • Enables the selection of appropriate components (resistors, power supplies) to ensure safe and efficient operation

Power and Electric Fields in Circuits

• Power in an electrical circuit represents the rate of energy transfer
  • Calculated using the formula $P = VI$, where $P$ is power in watts (W)
  • Relates to Ohm's law through the equations $P = I^2R$ and $P = \frac{V^2}{R}$
• Electric fields in circuits drive the flow of charge
  • The strength of the electric field is proportional to the voltage gradient
  • Influences the behavior of charge carriers in the circuit