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PHYSICS • ELECTRICITY

Series & Parallel Circuits

Switch topology while preserving the same source and resistors, inspect branch current and voltage, compare both networks at once and tune the circuit to a target total current.

● LIVE TOPOLOGY LABSeries • 0.400 A total
Equivalent resistance30.00 Ω
Total current0.400 A
Opposite topology current1.800 A
Total power4.80 W
Target error0.000 A
Kirchhoff check0.000000

Total current versus voltage

series and parallel on the same axes

Compare topology without changing components

The same source and resistors are evaluated in both networks, so topology becomes the only conceptual change. Branch current, voltage drop and resistor power remain visible instead of being compressed into equivalent resistance alone.

Fast investigations

  1. Use equal resistors and compare series versus parallel equivalent resistance.
  2. In series, verify I₁ = I₂ while voltage divides.
  3. In parallel, verify V₁ = V₂ while current divides.
  4. Use the target-current challenge to design multiple networks that satisfy the same load current.

LEARN WITH THE SIMULATION

Understand Series & Parallel Circuits by experimenting.

START HERE

Series and parallel resistor networks obey the same conservation laws but distribute voltage and current differently. Equivalent resistance summarizes how the entire network appears to a source.

BUILD THE IDEA

What you should understand first

  • Calculate equivalent resistance in series and parallel.
  • Compare total current for the same source voltage.
  • Understand branch current in a parallel network.

TRY IT YOURSELF

Which arrangement draws more total current from the same voltage source?

  1. Set two resistor values and note the series equivalent resistance.
  2. Switch to parallel without changing the resistors or source.
  3. Compare equivalent resistance and total current.
Read the visual:

The parallel arrangement has lower equivalent resistance and therefore draws more current from an ideal fixed-voltage source.

WHY IT WORKS 01

Calculate equivalent resistance in series and parallel.

Series and parallel resistor networks obey the same conservation laws but distribute voltage and current differently. Equivalent resistance summarizes how the entire network appears to a source. Focus on the relationship between the controlled variable and the measured response rather than treating the visual change as the explanation.

WHY IT WORKS 02

Compare total current for the same source voltage.

The parallel arrangement has lower equivalent resistance and therefore draws more current from an ideal fixed-voltage source. Use an extreme or boundary setting after the baseline trial to check whether the same reasoning still holds.

DO NOT MIX THESE UP

Common misconception

Series resistances add directly; parallel resistances do not. Current is the same through series elements but splits among parallel branches. Voltage distribution depends on topology.

PRACTICE CHALLENGE

Which arrangement draws more total current from the same voltage source?

  • Set two resistor values and note the series equivalent resistance.
  • Switch to parallel without changing the resistors or source.
  • Compare equivalent resistance and total current.
Reveal the reasoning

The parallel arrangement has lower equivalent resistance and therefore draws more current from an ideal fixed-voltage source. Series resistances add directly; parallel resistances do not. Current is the same through series elements but splits among parallel branches. Voltage distribution depends on topology.

MODEL BOUNDARIES

What this simulation assumes

Every simulation simplifies reality or a mathematical system. These are the assumptions and limits to keep in mind while interpreting the results.

Model assumptions

  • Resistors are ideal, linear and time-invariant.
  • The source is ideal and wires have zero resistance.
  • The circuit is treated as a steady-state resistive network.

Model limitations

  • Capacitance, inductance, source internal resistance and component tolerances are ignored.
  • Real components can heat up and change resistance with current and temperature.

CONNECT IT

Where this matters

  • Household wiring
  • Sensor networks
  • Electronic circuit design

WORDS THAT MATTER

Key vocabulary

Equivalent resistance
Single resistance with the same source behavior as the network.
Branch
One path through a parallel network.
Series
Components connected along one current path.