Electrical Circuits Basics

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Questions and Answers

What is the mathematical representation of Ohm's Law?

  • I = R/V
  • I = V/R (correct)
  • V = IR
  • R = V/I

According to Kirchhoff's Current Law, what is the relationship between the sum of currents entering a node and the sum of currents leaving a node?

  • The sum of currents entering a node is less than the sum of currents leaving a node
  • The sum of currents entering a node is equal to the sum of currents leaving a node (correct)
  • The sum of currents entering a node is greater than the sum of currents leaving a node
  • The sum of currents entering a node is inversely proportional to the sum of currents leaving a node

What is the total resistance of a series circuit consisting of three resistors with resistances 2Ω, 4Ω, and 6Ω?

  • 6Ω
  • 12Ω (correct)
  • 3Ω
  • 18Ω

What is the characteristic of a parallel circuit when one resistor is broken?

<p>The other resistors continue to operate (A)</p> Signup and view all the answers

What is the mathematical representation of the total resistance of a parallel circuit consisting of n resistors?

<p>1/R_total = 1/R1 + 1/R2 + ... + 1/Rn (B)</p> Signup and view all the answers

What is the time constant of an RC circuit?

<p>The time taken for the capacitor to charge or discharge to 63.2% of its final value (D)</p> Signup and view all the answers

What is the characteristic of a series circuit when one resistor is broken?

<p>The entire circuit is broken (C)</p> Signup and view all the answers

According to Kirchhoff's Voltage Law, what is the sum of voltage changes around a closed loop?

<p>The sum of voltage changes is zero (C)</p> Signup and view all the answers

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Study Notes

Ohm's Law

  • States that the current flowing through a conductor is directly proportional to the voltage applied across it, provided the temperature remains constant.
  • Mathematically represented as: I = V/R
  • Where:
    • I is the current in amperes (A)
    • V is the voltage in volts (V)
    • R is the resistance in ohms (Ω)

Kirchhoff's Laws

  • Two laws that describe the behavior of electric circuits:
    1. Kirchhoff's Current Law (KCL)
      • States that the sum of currents entering a node is equal to the sum of currents leaving a node.
      • Mathematically represented as: ΣI_in = ΣI_out
    2. Kirchhoff's Voltage Law (KVL)
      • States that the sum of voltage changes around a closed loop is zero.
      • Mathematically represented as: ΣV = 0

Resistors In Series

  • A series circuit consists of resistors connected one after the other.
  • Characteristics:
    • The current is the same throughout the circuit.
    • The total voltage is the sum of individual voltage drops across each resistor.
    • The total resistance is the sum of individual resistances.
    • If one resistor is broken, the entire circuit is broken.
  • Mathematically represented as: R_total = R1 + R2 + ... + Rn

Resistors In Parallel

  • A parallel circuit consists of resistors connected between the same two nodes.
  • Characteristics:
    • The voltage is the same across each resistor.
    • The total current is the sum of individual currents through each resistor.
    • The total resistance is less than the individual resistances.
    • If one resistor is broken, the others continue to operate.
  • Mathematically represented as: 1/R_total = 1/R1 + 1/R2 + ... + 1/Rn

RC Circuits

  • A circuit consisting of resistors and capacitors.
  • Characteristics:
    • The capacitor stores energy in the form of an electric field.
    • The resistor controls the rate of charging and discharging of the capacitor.
    • The time constant (Ï„) is the time taken for the capacitor to charge or discharge to 63.2% of its final value.
    • Mathematically represented as: Ï„ = RC

Ohm's Law

  • Current flowing through a conductor is directly proportional to the voltage applied, provided temperature remains constant.
  • Mathematically represented as: I = V/R
  • I: current in amperes (A)
  • V: voltage in volts (V)
  • R: resistance in ohms (Ω)

Kirchhoff's Laws

Kirchhoff's Current Law (KCL)

  • Sum of currents entering a node is equal to the sum of currents leaving a node.
  • Mathematically represented as: ΣI_in = ΣI_out

Kirchhoff's Voltage Law (KVL)

  • Sum of voltage changes around a closed loop is zero.
  • Mathematically represented as: ΣV = 0

Resistors In Series

  • Series circuit consists of resistors connected one after the other.
  • Current is the same throughout the circuit.
  • Total voltage is the sum of individual voltage drops across each resistor.
  • Total resistance is the sum of individual resistances.
  • If one resistor is broken, the entire circuit is broken.
  • Mathematically represented as: R_total = R1 + R2 +...+ Rn

Resistors In Parallel

  • Parallel circuit consists of resistors connected between the same two nodes.
  • Voltage is the same across each resistor.
  • Total current is the sum of individual currents through each resistor.
  • Total resistance is less than the individual resistances.
  • If one resistor is broken, the others continue to operate.
  • Mathematically represented as: 1/R_total = 1/R1 + 1/R2 +...+ 1/Rn

RC Circuits

  • Circuit consisting of resistors and capacitors.
  • Capacitor stores energy in the form of an electric field.
  • Resistor controls the rate of charging and discharging of the capacitor.
  • Time constant (Ï„) is the time taken for the capacitor to charge or discharge to 63.2% of its final value.
  • Mathematically represented as: Ï„ = RC

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