How to Solve a Combination Circuit (Easy)

How to Solve Combination Circuits

Introduction to Combination Circuits

• Mr. M introduces the lesson on solving combination circuits, which contain both series and parallel circuit properties.

• The main strategy involves condensing the circuit into either a series or parallel configuration, requiring knowledge of the rules for each type.

Example 1: Condensing to Series Circuit

• The first example features a series resistor combined with two parallel resistors that need to be condensed into a series-only circuit.

• To condense the parallel resistors, use the formula 1/R_total = 1/R_2 + 1/R_3 , resulting in one equivalent resistor (R23).

Example 2: Condensing to Parallel Circuit

• In this example, there are two branches with resistors in series within a parallel circuit.

• Resistors in series are added using R_total = R_1 + R_2 , leading to new equivalent resistors (R12 and R34).

Full Example Walkthrough

• A combination circuit is presented where voltage, current, and resistance must be calculated for each resistor.

• The first step is condensing two resistors in series (R2 and R3), yielding an equivalent resistance of 5 ohms.

Final Calculations and Current Flow

• After further condensation of resistors in parallel (5 ohm each), total resistance is calculated as 4.5 ohms.

• Using Ohm's Law ( V = I times R ), total current is determined as approximately 2.67 amps.

Voltage Distribution Across Resistors

• Current through R1 remains constant at 2.67 amps since it’s a series connection; voltage across it is calculated as 5.34 volts.

• The remaining voltage across other components is found by subtracting from total voltage (12V - 5.34V = 6.66V).

Analyzing Parallel Branches

• In the parallel branches, voltages remain equal at 6.66 volts; however, they distribute differently based on individual resistor values.

• Current through one branch can be calculated using Ohm's Law again for accurate results.

Understanding Current in Parallel Circuits

Calculating Current Distribution

• The total current in the circuit is 2.67 amps, and to find the current down a specific branch, subtract the known current (1.3 amps) from the total: 2.67 - 1.3 = 1.37 amps.

• Both branches of the parallel circuit have equal resistance (5 ohms), leading to an equal distribution of current across them.

Voltage Calculation in Series

• In a series configuration, all currents remain constant; thus, both resistors carry a current of 1.3 amps.

• The voltage across each resistor can be calculated by multiplying resistance by current: for one resistor, 2 times 1.3 = 2.6 volts; for another, 3 times 1.3 = 3.9 volts.

Verifying Total Voltage

• The sum of voltages across both resistors should equal the total voltage supplied (6.6 volts). Due to rounding errors, it may show as approximately 6.5 volts.

• It’s emphasized that both branches in parallel must maintain the same voltage level throughout.

Key Strategies for Circuit Analysis

• Two main strategies are highlighted: condensing combination circuits and ensuring consistent application of rules regarding series and parallel configurations.