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Summary of Electricity: Parallel Resistors

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Physics

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Electricity: Parallel Resistors

TOPICS

Keywords

  • Electricity
  • Resistors
  • Parallel
  • Equivalent Resistance
  • Voltage Difference (DDP)
  • Current Intensity
  • Ohm's Law
  • Parallel Circuit

Key Questions

  • How to calculate the equivalent resistance in a parallel resistor circuit?
  • How does the voltage difference (DDP) affect each resistor in a parallel circuit?
  • What is the relationship between the total current and the currents in the branches of a parallel circuit?

Crucial Topics

  • Each resistor in a parallel circuit has the same voltage difference (voltage) as the source.
  • The total current is the sum of the currents through each parallel resistor.
  • The equivalent resistance in a parallel circuit is always less than the resistance of any of the individual resistors.

Fundamental Formulas

  • Ohm's Law: V = I * R
  • Calculation of Equivalent Resistance in Parallel: 1/Req = 1/R1 + 1/R2 + ... + 1/Rn
  • Total Current in the Circuit: Itotal = I1 + I2 + ... + In
  • Voltage Difference in Parallel Resistors: Vtotal = V1 = V2 = ... = Vn

NOTES

Key Terms

  • Electricity: Phenomenon associated with the presence and flow of electric charge.
  • Resistors: Components that offer resistance to the passage of electric current, converting electrical energy into heat.
  • Parallel: Circuit configuration where two or more components are connected in multiple current paths.
  • Equivalent Resistance (Req): Represents the total resistance of a circuit, replacing all resistors with a single resistor with equivalent resistance.
  • Voltage Difference (DDP): Also known as voltage, it is the electrical potential energy per unit of charge that drives the electric current.
  • Current Intensity: Amount of electric charge that passes through a point in the circuit in one second, measured in amperes.
  • Ohm's Law: Relationship between voltage (V), current (I), and resistance (R) in a circuit, expressed by the formula V = I * R.
  • Parallel Circuit: Type of circuit where the components are connected so that the voltage is the same across all of them.

Main Ideas and Concepts

  • The voltage across all resistors in parallel is identical, equal to the voltage from the power source.
  • Total Current: The value of the total current flowing through a parallel circuit is the sum of the currents flowing through each independent path.
  • Importance of equivalent resistance: While the total resistance decreases, the total current in the circuit increases, illustrating an inverse characteristic of the resistance-current relationship.

Topic Contents

  • Equivalent Resistance in Parallel: To calculate the equivalent resistance, we add the inverses of the individual resistances and take the inverse of the result.
    • Practical example: If R1 = 100Ω and R2 = 200Ω, then 1/Req = 1/100 + 1/200, or 1/Req = 0.01 + 0.005 = 0.015. Therefore, Req = 1/0.015 ≈ 66.67Ω.
  • Ohm's Law in Parallel Circuit: Applying V = I * R for each resistor, the same voltage will result in different currents depending on the individual resistance.
  • Current Distribution: The current entering a node (connection point in a circuit) is equal to the current leaving the node, according to Kirchhoff's first law, or the node law.

Examples and Cases

  • Current Calculation Example: Given a 10V voltage source connected to two resistors in parallel, R1 = 2Ω and R2 = 5Ω, we calculate the total current.
    • Current in R1: I1 = V/R1 = 10V/2Ω = 5A
    • Current in R2: I2 = V/R2 = 10V/5Ω = 2A
    • Total Current: I_total = I1 + I2 = 5A + 2A = 7A
  • DDP Example in Parallel: Two resistors, R1 and R2, are in parallel with a DDP of 9V from the source. Both resistors are subject to this same voltage, regardless of their resistance values.

SUMMARY

Summary of the most relevant points

  • The Voltage Difference (DDP) is constant across all resistors in a parallel circuit, equal to the voltage supplied by the source.
  • The Equivalent Resistance (Req) in a parallel circuit is calculated by summing the inverses of the individual resistances: 1/Req = 1/R1 + 1/R2 + ... + 1/Rn.
  • In a parallel circuit, the Total Current (Itotal) is equal to the sum of the currents in each individual path: Itotal = I1 + I2 + ... + In.
  • Ohm's Law serves as the basis for understanding how voltage relates to current and resistance in each part of the circuit.

Conclusions

  • Understanding of Parallel Circuits: The equivalent resistance in a parallel circuit will always be less than the smallest of the circuit's resistances.
  • Current and Voltage Analysis: It is understood that the voltage is the same across each resistor, while the currents vary according to individual resistances.
  • Problem Solving: The calculation of equivalent resistance and Ohm's Law are applied to solve problems involving resistors in parallel.
  • Inverse Relationship: The inverse relationship between equivalent resistance and total current in the circuit is recognized – the lower the equivalent resistance, the greater the current flowing in the circuit.

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