Electrical circuits operate based on the existence of a complete path for current to flow. A closed circuit provides an unbroken route that allows charge to move, while an open circuit interrupts this path, preventing any flow.
In physical terms, current can only circulate when all connections are intact, forming a continuous loop from source to load and back again. Within a structured flow perspective, circuits are understood as path-dependent systems—where the presence or absence of continuity determines whether flow is possible.
Path Completion as a Flow Condition
This flow reframes open and closed circuits as conditions that enable or disable system behaviour. A closed path allows energy transfer and system operation, while an open path halts all flow, defining an inactive state.
Closed circuits enable continuous current flow
Open circuits prevent charge movement entirely
Defines fundamental system states: active or inactive
By viewing circuits in terms of path completion, system behaviour can be understood at its most fundamental level. This perspective provides the foundation for analysing how all electrical systems operate, from simple switches to complex networks.
How to Use This Teaching Flow
This page includes an executable teaching flow that can run inside any modern AI system (ChatGPT, Google AI, Claude, and others). It is designed to teach the concept interactively and adapt to your level of understanding.
Quick Start
1. Copy the full Flow Algebra code below.
2. Paste it into your preferred AI chat.
3. Ask the AI to teach you the concept or start the lesson.
Example Prompts
“Teach me this step by step.”
“Explain this like I’m new to the topic.”
“Test my understanding after the explanation.”
“Give me a real-world example.”
What Makes This Different
The AI adapts to your understanding as you respond
It changes explanation depth, pace, and style automatically
It checks your understanding and reinforces where needed
It maintains scientific accuracy while simplifying concepts
Tip
The more you interact (ask questions, answer checks, request examples), the better the system adapts to you.
Flow: OpenVsClosedCircuits_PathCompletion_v1_0
Purpose:
Model open and closed circuits as fundamental states of path continuity, enabling structured teaching of how electrical flow depends on whether a conductive path is complete or broken.
System:
S = (I, R, B, K)
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Teaching Directive
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Execution_Mode:
Teaching
Audience:
Beginner to Intermediate learner
Teaching_Flow:
Explain → Visualise → Formalise → Apply
Instruction:
- Begin with intuitive explanation of a circuit as a path for charge to flow
- Explain that a closed circuit forms a complete loop allowing current
- Explain that an open circuit breaks the loop and stops current
- Relate open and closed states to switches and real-world devices
- Reinforce with simple battery-wire-lamp examples
Constraints:
H = ∅
Clarity before formalism
Goal:
Student understands that:
- current requires a complete path to flow
- a closed circuit enables current
- an open circuit prevents current
- circuit behaviour depends on path continuity
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State
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I = {
source_voltage,
circuit_path,
continuity_state,
open_points,
closed_points,
current_value,
load_condition,
connection_state,
control_elements,
time_state
}
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Rules
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R = {
detect_path_structure,
evaluate_continuity,
identify_open_or_closed_state,
permit_current_flow_if_closed,
block_current_flow_if_open,
update_load_response,
apply_control_element_changes
}
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Boundaries
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B = {
circuit_path_defined,
source_condition_required_for_current,
conductive_material_required_for_path,
continuity_state_must_be_determinable,
no_unphysical_current_in_open_path,
no_unphysical_blocking_in_valid_closed_path
}
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Invariants
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K = {
closed_circuit_implies_complete_conductive_loop,
open_circuit_implies_broken_path,
current_requires_closed_path,
open_path_results_in_zero_current_in_that_branch,
closed_path_allows_current_if_source_present,
path_continuity_directly_controls_circuit_behaviour,
switches_and_faults_change_continuity_state
}
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Execution
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E_t = expand(I, R)
V_t = {
x ∈ E_t | x satisfies (B ∧ K)
}
Selection:
x* = argmax_(x ∈ V_t) P(x | I, R, B, K)
Update:
I_(t+1) = update(I_t, x*)
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Output
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O = circuit_behaviour_determined_by_path_continuity | (B, K)
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Failure Condition
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V_t = ∅ ⇒ O = FAIL
Meaning:
If no valid circuit path, continuity condition, or source relationship can be established, no coherent open or closed circuit behaviour can be evaluated.
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Interpretation
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An electrical circuit must form a complete loop for current to flow. When the path is closed, charge can move continuously from the source, through the circuit, and back to the source. When the path is open, this loop is broken, and current cannot flow.
This concept is fundamental to all electrical systems. Devices such as switches control whether a circuit is open or closed, and faults such as broken wires also create open circuits. Understanding path completion is essential for analysing, designing, and troubleshooting circuits.
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Core Relations
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Closed path:
current flow possible
Open path:
current = 0 in that path
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Derived Relations
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Closed circuit with source:
load can operate
Open circuit anywhere in loop:
entire loop current stops
Switch control:
changes between open and closed states
Continuity:
required for sustained charge flow
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Teaching Outcome
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Student can:
- Understand the difference between open and closed circuits
- Explain why current requires a complete path
- Relate switches to circuit continuity control
- Recognise faults as open circuit conditions
- Apply path completion reasoning to simple circuits
Power captures the rate at which energy is transferred within a system.
This section explores how voltage and current combine to produce real energy flow, revealing how systems do work, dissipate energy, and operate over time.
