Circuit expansion is the reverse process of circuit breakdown. After finding the equivalent resistance, we work backwards to determine the current and voltage across each individual resistor. This is essential for understanding how power is distributed throughout a circuit.
What is Circuit Expansion?
Circuit Expansion: The process of working backwards from the equivalent resistance to find current and voltage across each individual resistor in the original circuit.
Circuit expansion involves:
Starting Point: Known equivalent resistance and total current
Reverse Process: Working backwards through each combination step
Current Division: Finding how current splits in parallel branches
Voltage Division: Finding how voltage drops across series resistors
In my opinion, circuit expansion is a lot more difficult than circuit breakdown. It is a lot more difficult to keep track of the current and voltage at each step. It is also a lot more difficult to verify your work. However, it is a very important skill to have for AP Physics C.
This video will walk you through the process of circuit expansion step by step.
Key Takeaways Summary
🎯 Essential Circuit Expansion Steps
Start: Use equivalent resistance and total current from breakdown
Expand Series: Same current, voltage divides: V = IR
Expand Parallel: Same voltage, current divides: I = V/R
Work Backwards: Reverse the breakdown process step by step
Verify: Check voltage and current conservation
⚡ Key Formulas for Expansion
Total Current: I_total = V_battery / R_eq
Series Current: I_series = I_total (same for all)
Series Voltage: V_i = I_total × R_i
Parallel Voltage: V_parallel = V_total (same for all)
Parallel Current: I_i = V_total / R_i
🔍 Expansion Rules
Series: Current constant, voltage divides proportionally
Parallel: Voltage constant, current divides inversely to resistance
Power: P = I²R = V²/R = IV for each resistor
Conservation: Total voltage = sum of voltage drops
✅ Verification Methods
Voltage Check: Sum of voltage drops = battery voltage
Current Check: Sum of parallel currents = total current
Power Check: Sum of individual powers = total power
Ohm's Law: V = IR must hold for each resistor
💡 Pro Tips for Expansion
Start Simple: Begin with the equivalent circuit
Track Carefully: Keep track of current and voltage at each step
Use Tables: Organize results in a table for clarity
Verify Each Step: Check conservation laws at each expansion
Practice Regularly: Expansion becomes easier with practice