Series and Parallel Circuits

Series and Parallel Circuits Defined

• Series Circuit: An electric circuit whose component parts are arranged end-to-end so that the current passes consecutively through each part.

• Parallel Circuit: An electric circuit where the component parts are connected as branches of the main circuit, allowing the current to be divided among them.

Example: Christmas Lights

• Series Connection: If one bulb fails, all bulbs go out (one line - current must pass through each).

• Parallel Connection: If one bulb burns out, others remain lit (separate lines - current can bypass burned out bulb).

Rules for Simple Series Circuits

• Total Resistance: The total resistance (RT) is equal to the sum of the individual resistances:

  • RT = R1 + R2 + R3

• Current: The current (IT) through each element is the same:

  • IT = I1 = I2 = I3

• Voltage: The sum of the voltages (VT) across each element equals the total voltage:

  • VT = V1 + V2 + V3

Series Circuit Formula

• Current: IT = I1 = I2 = I3

• Voltage: VT = V1 + V2 + V3

• Resistance: RT = R1 + R2 + R3

Rules for Parallel Circuit

• Total Current: The sum of the currents is equal to the total circuit current:
  IT = I1 + I2 + I3

• Voltage: The voltage across each circuit element is the same:
  VT = V1 = V2 = V3

• Total Resistance: The total resistance is the inverse of the sum of the reciprocals of each individual resistance:
  1/RT = 1/R1 + 1/R2 + 1/R3 orrrr RT= 1/(1/R1 + 1/R2 + 1/R3) orrrr RT= flipping the final summed up fraction

Parallel Circuit Total Resistance

• In a parallel circuit, current is divided among branches, making total resistance less than that of an individual path.

• Adding more resistors in parallel increases the total cross-sectional area, thus decreasing total resistance.

  • Example: If resistances are 1, 2, and 3 ohms:
    RT = rac{1}{ rac{1}{1} + rac{1}{2} + rac{1}{3}} = rac{1}{1 + 0.5 + 0.333} = rac{1}{1.833} ext{ (Calculate to get)} RT ext{ approximately } 0.55 ext{ ohms}

Review Problems Using Series Circuit Rules

1. Total current in a series circuit with 3 resistances, each supplied with 10 amperes? Answer: 10 amperes

2. Total voltage in a series circuit with 3 resistances, each at 10 volts? Answer: 30 volts

3. Total resistance of a series circuit with resistances of 2.5Ω, 4.2Ω, and 6.8Ω? Answer: 13.5Ω (Calculation: 2.5 + 4.2 + 6.8 = 13.5)

Review Problems Using Parallel Circuit Rules

1. Total current in a parallel circuit with 3 resistances, each at 10 amperes? Answer: 30 amperes

2. Total voltage in a parallel circuit with 3 resistances, each at 10 volts? Answer: 10 volts

3. Total resistance of a parallel circuit resistances of 2.5Ω, 4.2Ω, and 6.8Ω? Answer:

   • Calculation: rac{1}{ rac{1}{2.5} + rac{1}{4.2} + rac{1}{6.8}}

     • Result: = 1.26Ω

Summary of Total Resistance Calculations

• Parallel Circuit: For resistors of 10Ω, 10Ω, 20Ω: Total Resistance: 4Ω

• Series Circuit: For the same resistors: Total Resistance: 40Ω