Series and Parallel Circuits

Series Circuits

• Definition: In a series circuit, components are connected end-to-end, forming a single path for current to flow.

• Configuration:

  • Resistor arrangement: Resistor 1, Resistor 2, Resistor 3 in sequence.

  • The voltage of the battery equals the total voltage across all components.

• Current Flow:

  • Current flows through all components sequentially; it cannot split into multiple paths.

  • Total current (I) remains constant through every resistor: I = I1 = I2 = I3.

• Voltage Drop:

  • Voltage is consumed across each component. Total voltage (VT) = V1 + V2 + V3.

• Total Resistance (RT):

  • Calculation: RT = R1 + R2 + R3 (simple addition of resistances).

Parallel Circuits

• Definition: In a parallel circuit, components are connected across common points creating multiple paths for current.

• Configuration:

  • Resistors are arranged in parallel paths connected to the same voltage supply.

• Current Flow:

  • Total current (IT) from the battery splits among different paths: IT = I1 + I2 + I3.

  • Current can be different in each path depending on resistance: I1, I2, and I3 may not be equal.

• Voltage:

  • Voltage across each resistor is the same and equals battery voltage (V = VT).

• Total Resistance (RT):

  • Calculation: 1/RT = 1/R1 + 1/R2 + 1/R3 (using reciprocal method).

Comparing Series and Parallel Circuits

• Resistance:

  • Series: Total resistance equals the sum of individual resistances.

  • Parallel: Total resistance is calculated using the reciprocal formula.

• Current:

  • Series: Same current flows through all components.

  • Parallel: Current divides among paths; sum equals total current from the battery.

• Voltage:

  • Series: Total voltage divided among components.

  • Parallel: Constant voltage across all components equal to the battery voltage.

Example Calculation (Series Circuit)

• Given: 12V battery, Resistor 1 = 20 Ohms, Resistor 2 = 100 Ohms.

• Total Resistance:

  • RT = R1 + R2 = 20 Ohms + 100 Ohms = 120 Ohms.

• Calculate Current:

  • Total Current (I) = Total Voltage / Total Resistance = 12V / 120 Ohms = 0.1 Amps.

• Voltage across each Resistor:

  • Voltage for Resistor 1 (V1) = I * R1 = 0.1 Amps * 20 Ohms = 2V.

  • Voltage for Resistor 2 (V2) = I * R2 = 0.1 Amps * 100 Ohms = 10V.

• Summary: Voltage across resistors sums to total voltage: V1 + V2 = 2V + 10V = 12V (accounts for rounding.)