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Passive sign convention
An assumption of: the sign of the current RELATIVE to the voltage for passive circuit elements.
ASSUME: positive current enters the node at the higher voltage
ESSENTIALLY: You can assume (arbitrarily) EITHER the voltage polarity, OR the current direction. This assumption dictates the assumed direction of the other parameter. These assumptions provide REFERENCE voltage polarities and current directions.
3 Steps to assign passive sign convention. (and what not to do)
DON'T try to figure out the "correct" voltage polarities or current directions before performing the analysis.
- 1. Arbitrarily assign EITHER the assumed voltage polarity OR the current direction.
- 2. Label the other characteristic for the passive circuit element so that they agree with the passive sign convention.
- 3. Perform the analysis using the assumed signs! Negative values indicate that the assumption you made was wrong, so switch up the assumed direction of either the current or of the voltage polarity.
How to provided voltage sources affect the choice of the passive sign convention?
Charge (q) is the basic quantity in circuit analysis
Unit: Coulombs. 1 Coulomb = -6.24 10^18 electrons
Current (i) is the rate of change of charge with time:
UNITS: Amperes (coulombs/second)
i = dq/dt
If you're sitting at some point in you're circuit and watching electrons go by, the rate at which they're going by gives you the current!
Voltage (v): Voltage quantifies the change in energy of a unit charge at two different physical locations.
v = dW/dq
Units: Volts (V) => Joules/coulomb
Power is the rate of change of energy with time
P = dW/dt = dW/dq x dq/dt = (v)(i) [voltage times current]
Passive Circuit element
Total energy delivered to the circuit element by the rest of the circuit is non-negative.
Passive element can STORE or DISSIPATE energy but it cannot CREATE energy.
Active Circuit element
Active circuit elements can supply energy to the circuit from external sources.
Giga, Mega, Kilo
Giga = 10^9
Mega = 10^6
Kilo = 10^3
Micro, Nano, Pico
Micro = 10^-6
Nano = 10^-9
pico = 10^-12