Electric Circuits: Resistance

Electric Circuits: Resistance

Ohm’s Law

  • Ohm’s Law states that the current flowing through a conductor between two points is directly proportional to the voltage across the two points.
  • This law introduces the concept of resistance (R), which is equal to the ratio of voltage across the element (V) to the current through the element (I). Mathematically, this is expressed as: R = V/I.

Resistivity

  • Resistivity (ρ) is a property of a material that measures its opposition to the flow of electric current.
  • It is defined as the resistance of a unit cube of the material and is given by R = ρ(L/A), where L is the length and A is the cross-sectional area.

Factors Affecting Resistance

  • The resistance of a component is affected by its length, cross-sectional area, and resistivity. A longer or thinner component, or one made from a material with higher resistivity, will have a higher resistance.
  • Similarly, the resistance of a wire increases with temperature, because as temperature increases, the ions vibrate more and hinder the flow of electrons.

Series and Parallel Circuits

  • In a series circuit, the total resistance is equal to the sum of the individual resistances: R_total = R1 + R2 + …
  • In a parallel circuit, the total resistance is found using the formula: 1/_R_total = 1/R1 + 1/R2 + ..
  • The total resistance of a parallel circuit is always less than the smallest resistance in the circuit.

Power in Circuits

  • Power (P) in an electrical circuit is given by P = VI, where V is the potential difference across the component and I is the current through the component.
  • It can also be found using P = I²R or P = V²/R, depending on the information available.

Energy in Circuits

  • The energy transferred (E) from electrical energy to other forms in a circuit can be calculated using E = VIt, where V is potential difference, I is current, and t is time in seconds.
  • If resistance and time are known, energy transferred can also be calculated using E = I²Rt or E = V²t/R.

Remember, understanding these key concepts around resistance and how they apply to different scenarios is essential in dealing with electric circuits. Happy revising!