11.5 Compound Direct Current Circuits

• In a series circuit, what is the relationship between the current through each resistor?

  The current is the same
• In parallel circuits, the total current is the sum of the individual branch currents
• In a parallel circuit, what is the relationship between the voltage across each resistor?

  The voltage is the same
• What is voltage division in parallel circuits?

  Voltage remains the same
• Kirchhoff's laws are essential for analyzing compound circuits.


  True
• Compound circuits can be classified into three types: series, parallel, and combined
• What laws are used to analyze compound circuits?

  Kirchhoff's Laws
• Steps to analyze a compound circuit using Kirchhoff's laws

  1️⃣ Identify closed loops and junctions

  2️⃣ Apply Kirchhoff's Voltage Law to each loop

  3️⃣ Apply Kirchhoff's Current Law to each junction

  4️⃣ Solve the resulting system of equations
• Match the circuit property with its characteristic:

  Total Resistance in Series ↔️ Sum of individual resistances

  Total Resistance in Parallel ↔️ Reciprocal of sum of reciprocals

  Total Current in Series ↔️ Same for all resistors

  Total Current in Parallel ↔️ Divides among resistors
• What is the total current in a parallel circuit?

  Sum of individual currents
• What happens to the total resistance in a series circuit if more resistors are added?

  It increases
• What is the sum of voltage drops around a closed loop in a circuit according to Kirchhoff's Voltage Law?

  Zero
• In a parallel circuit, the voltage is the same across each resistor
• The total resistance in a parallel circuit is the reciprocal of the sum of reciprocals
• What is the voltage across all resistors in a parallel circuit?

  Same across all resistors
• What does Kirchhoff's Current Law state?

  Sum of currents in equals sum of currents out
• The total resistance in a parallel circuit is the reciprocal of the sum of reciprocals
• In a series circuit, the current is the same through each resistor.


  True
• What does Kirchhoff's Voltage Law state?

  Sum of voltage drops equals zero
• In a parallel circuit, the total voltage is the same across all resistors
• What is the current through each resistor in a series circuit?

  The same
• How is current related in a series circuit?

  The same
• Which two laws are used to analyze combined circuits?

  Kirchhoff's Voltage Law and Kirchhoff's Current Law
• The current is the same for all resistors in a series circuit.


  True
• In a parallel circuit, the total current is the sum of the individual currents
• Match the circuit property with its correct characteristic:

  Series Circuit ↔️ Total resistance is the sum of individual resistances

  Parallel Circuit ↔️ Voltage is the same across all resistors

  Compound Circuit ↔️ Requires both KVL and KCL to analyze
• What type of circuit requires both Kirchhoff's Voltage Law and Kirchhoff's Current Law to analyze?

  Combined circuit
• What type of circuit combines series and parallel connections?

  Combined circuit
• Match the circuit property with its characteristic in series and parallel circuits:

  Current in Series ↔️ Same through all resistors

  Current in Parallel ↔️ Divides among resistors

  Total Voltage in Series ↔️ Sum of voltage drops

  Total Voltage in Parallel ↔️ Same across all resistors
• What laws are used to analyze series circuits?

  Ohm's Law and KVL
• In a combined circuit, series and parallel sections must be analyzed separately.


  True
• What is the sum of voltage drops around a closed loop in a circuit according to KVL?

  Zero
• Steps to solve a combined series-parallel circuit using KVL, KCL, and Ohm's Law:

  1️⃣ Apply KVL around the loop

  2️⃣ Apply KCL at the junction

  3️⃣ Use Ohm's Law for each resistor

  4️⃣ Solve the system of equations
• In a series circuit, the total resistance is the sum of individual resistances
• Match the circuit type with its characteristic:

  Series circuit ↔️ Current is the same through all resistors

  Parallel circuit ↔️ Voltage is the same across all resistors
• In a parallel circuit, the voltage across each resistor is the same.


  True
• The total resistance in a parallel circuit is the reciprocal of the sum of the reciprocals of individual resistances
• The equivalent resistance of two resistors in parallel is less than the resistance of either resistor.


  True
• According to Ohm's Law, voltage equals current times resistance
• Match the circuit parameter with its example value:

  Total Resistance ↔️ 4.67 Ω

  Total Current ↔️ 2.57 A