Electrical Circuits Basics

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 (τ) is the time taken for the capacitor to charge or discharge to 63.2% of its final value.
  • Mathematically represented as: τ = 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 (τ) is the time taken for the capacitor to charge or discharge to 63.2% of its final value.
• Mathematically represented as: τ = RC