19.2 Series Circuits

Series circuits are the foundation of electrical systems. They connect components in a single path, allowing current to flow through each element sequentially. Understanding series circuits is crucial for analyzing more complex electrical systems and troubleshooting common household circuits.

In series circuits, current remains constant while voltage divides among components. This concept is essential for designing circuits with specific voltage requirements and calculating power dissipation in electrical devices. Mastering series circuits paves the way for comprehending parallel and complex circuit configurations.

Series Circuits

Analysis of series circuits

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• Ohm's law establishes the relationship between voltage ($V$), current ($I$), and resistance ($R$) in a circuit as $V = IR$
  • Voltage measured in volts (V) represents the potential difference across a component
  • Current measured in amperes (A) represents the flow of electric charge through a component
  • Resistance measured in ohms ($\Omega$) represents the opposition to current flow in a component
• Equivalent resistance ($R_{eq}$) in series circuits is the sum of individual resistances: $R_{eq} = R_1 + R_2 + ... + R_n$
  • In series circuits, the current remains the same through all components as there is only one path for current to flow
  • The total voltage across a series circuit is equal to the sum of voltage drops across each individual component
• Current and voltage in series circuits can be calculated using Ohm's law
  • Current is determined by dividing the total voltage by the equivalent resistance: $I = \frac{V}{R_{eq}}$
  • Voltage drops across each component can be found using the current and individual resistances: $V_1 = IR_1$, $V_2 = IR_2$, etc.
• Power dissipated in each component can be calculated using $P = IV$ or $P = I^2R$

Interpretation of circuit diagrams

• Resistors in circuit diagrams are represented by zigzag lines with their resistance values labeled in ohms ($\Omega$)
  • Example: a resistor with a value of 100 $\Omega$ would be shown as a zigzag line with "100 $\Omega$" next to it
• Batteries are depicted as long and short parallel lines, with the longer line representing the positive terminal and the shorter line representing the negative terminal
  • The voltage of the battery is labeled in volts (V) next to the symbol
  • Example: a 9 V battery would have "9 V" written next to its symbol
• Switches are shown as a line with a break, representing the ability to open or close the circuit
  • An open switch indicates that the circuit is broken and no current can flow
  • A closed switch indicates that the circuit is complete and current can flow through the components
• Capacitors are represented by two parallel lines and store electric charge
  • The capacitance values are labeled in farads (F) next to the symbol
  • Example: a capacitor with a value of 10 microfarads would be shown as two parallel lines with "10 $\mu$F" next to it
• Circuit diagrams use standardized symbols to represent various components and their connections

Current and voltage in series circuits

• In series circuits, the current remains the same through all components as there is only one path for the current to flow
  • The current is determined by the total voltage supplied by the battery and the equivalent resistance of the circuit
  • Example: if a 12 V battery is connected to a series circuit with an equivalent resistance of 4 $\Omega$, the current through the circuit would be 3 A ($I = \frac{12 V}{4 \Omega} = 3 A$)
• The total voltage in a series circuit is equal to the sum of voltage drops across each individual component
  • Voltage drops across components depend on their individual resistances
    • Components with higher resistance will have larger voltage drops
    • Components with lower resistance will have smaller voltage drops
  • Example: in a series circuit with a 12 V battery and two resistors (6 $\Omega$ and 3 $\Omega$), the voltage drop across the 6 $\Omega$ resistor would be 8 V, and the voltage drop across the 3 $\Omega$ resistor would be 4 V
• Kirchhoff's voltage law states that the sum of voltage drops in a series circuit equals the total voltage supplied by the battery: $V_{battery} = V_1 + V_2 + ... + V_n$
  • This law is a consequence of the conservation of energy principle
  • Example: in the previous example, the sum of voltage drops (8 V + 4 V) equals the total voltage supplied by the battery (12 V)