ELECTENG 101 Chap.1 Electrical Quantities and Circuit Laws
Electrical Quantities and Circuit Laws
Build the signed language used throughout the course. Current needs a reference arrow, voltage needs a polarity, and power direction follows the passive sign convention. Kirchhoff current law conserves charge at a node, while Kirchhoff voltage law conserves energy per unit charge around a loop. The chapter turns a schematic into equations and closes every calculation with direction, unit and power balance.
These conventions make negative answers meaningful: they report that the physical direction opposes the chosen reference rather than proving the setup wrong. Ohm law supplies the component relation for each resistor, while topology determines which voltages and currents are shared. Open circuits enforce zero current and short circuits enforce zero voltage, two boundaries that must not be interchanged.
A complete solution therefore preserves labels from the diagram through the algebra, checks every unit, and tests whether total supplied and absorbed power balance.
What this chapter covers
- 01
Charge flow and current references
- 02
Voltage polarity and common reference
- 03
Resistance and Ohm law
- 04
Signed power and passive convention
- 05
Kirchhoff current and voltage laws
- 06
Open- and short-circuit boundaries
Worked example · free
A signed two-source loop
- +3KVL gives 10 − 2i − 4i − 4 = 0, hence i = 1 A clockwise.
- +2Current enters the positive terminal of the 4 V source, so it absorbs 4 W.
- +1Power supplied and absorbed both total 10 W.
Key terms
- Current reference
- An assigned arrow that defines the positive direction for a current variable.
- Passive convention
- A sign convention where current entering a positive-labelled terminal gives positive absorbed power.
- Node
- A set of conductively connected points sharing one electric potential.
- Loop
- A closed path through a circuit used to write a voltage balance.
Electrical Quantities and Circuit Laws FAQ
Why can circuit current be negative?
A negative result means the physical current runs opposite to the arrow chosen before solving. The reference remains valid; translate the sign into a direction instead of restarting the calculation. Keep the original arrow when checking KCL, because silently reversing it after seeing the answer changes the meaning of every term that used that current.
Can a voltage source absorb power?
Yes. If current enters the source terminal labelled positive, the passive sign convention gives positive absorbed power. Source symbols specify voltage or current, not an automatic energy direction. Rechargeable batteries and one ideal source driven by another are familiar cases in which a source-shaped element can receive energy from the rest of the circuit.
What should I check after KCL or KVL?
Substitute the solved values into the original equations, confirm units, test node or loop balance and verify that total signed power sums to zero for the complete circuit. Also translate each negative value into a physical direction and compare limiting cases, since a dimensionally correct number can still come from a reversed polarity or the wrong branch resistance.
How are KCL and KVL different?
KCL is written at a node and states that charge does not accumulate there in the lumped circuit model, so entering and leaving currents balance. KVL is written around a closed path and balances voltage rises and drops. They express different conservation statements and can be used together without duplicating the same equation.
When does Ohm law use a negative sign?
The resistor relation is positive when current enters the terminal labelled positive: v equals Ri. If the chosen current enters the terminal labelled negative, the same labelled voltage satisfies v equals minus Ri. The resistor has not become negative; the sign records that the voltage and current references do not follow the passive convention.
What is the safest way to write a loop equation?
Choose a traversal direction, mark every element polarity, and record each crossing as a rise or drop in that order. Do not decide signs from whether an element is called a source or resistor. After one full circuit, the algebraic sum must be zero, and reversing the traversal should produce the same equation multiplied by minus one.
Exam move
Redraw five small circuits and assign every current arrow and voltage polarity before solving. For each, write one KCL equation, one KVL equation and the signed power of every element. Deliberately reverse one reference and confirm that the physical conclusion stays unchanged after interpreting the negative result. Finish with open- and short-circuit limiting cases so zero current and zero voltage do not become confused.
Build a three-column error log headed reference, equation and interpretation. When a result fails, identify which column changed first instead of repeating every calculation. Include a mixed-source loop, a two-node network and one circuit whose source absorbs power. On a second pass, solve each network with different valid references and compare only the final physical statements.
Time a final drill in which every answer includes magnitude, unit and direction. This routine makes sign control visible and prepares the same notation used later for node voltage, op-amp summing equations, motor power flow and AC phase comparisons. Add a power-balance table that lists every element under supplied or absorbed energy flow and confirms the two columns agree before the solution is considered complete.
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