Resistors in Series

What You Need to Know

  • Ability to calculate current, voltage, and resistance in parallel and series DC circuits.

Series Circuits

  • Series connections: Components connected one after another in the same loop.

  • Current flows through each component in series is the same.

  • Example: Two lamps in series - if one lamp fails, the other won’t light (e.g., Christmas tree lights).

  • Series connections are essential for circuit breakers or fuses to function correctly.

Key Facts About Series Circuits

  1. Current is the same throughout.

  2. Voltages add up to the supply voltage.

Current in Series Circuits

  • Same current flows through each resistor (I1 = I2 = I3).

Voltage in Series Circuits

  • Total voltage equals the sum of individual voltages across each resistor (VT = V1 + V2 + V3, known as Kirchoff's Law).

Resistance in Series Circuits

  • Total resistance is the sum of all individual resistances: RT = R1 + R2 + R3.

Summary Formulas for Series Circuits

  • Current: I1 = I2 = I3; Voltage: VT = V1 + V2 + V3; Resistance: RT = R1 + R2 + R3.

Important Notes

  • Adding components in series increases total resistance.

Example Calculations

  • Example 1:

    • Calculate total resistance: R1 = 20, R2 = 50, R3 = 80, R4 = 30; RT = 20 + 50 + 80 + 30 = 180 Ohms.

  • Example 2:

    • Calculate current: with R1 = 20, R2 = 30, R3 = 70 and a supply of 24 volts.

    • RT = 20 + 30 + 70 = 120 Ohms; I = V/R = 24/120 = 0.2A.

  • Example 3:

    • Calculate potential across a resistance: With R = 230 Ohms and I = 10 A, V = I x R = 10 x 230 = 2300 volts.

Application of Kirchoff’s Law

  • Verify that the sum of the voltages across each resistor equals the supply voltage.