Basic Linear Circuits Review

Common Measurements and Units

In the representations of measurements such as charge, voltage, current, and power, an uppercase letter (C, V, I, P) implies that it is constant, and a lowercase letter (c,v,i,p) implies that it is time-variant.

Charge (Coulomb)

Protons are positive charges, and electrons are negative charges. Charges in motion is a current. The SI unit for charge is the coulomb, which is equivalent to the amount of charge the current (in amperes) delivers in an amount of time (in seconds). 1 coulomb is equal to 1 ampere multiplied by 1 second.

$1C=(1A)\cdot (1s)$

Electric Potential (Volt)

The volt is a unit for the relative potential energy between two points or two electrodes. The ground is usually assigned a voltage of 0, and used as a reference. Current tends to flow from high voltage to low voltage. 1 volt is equal to 1 joule per coulomb.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1V=\frac{1J}{1C}}

Current (Ampere)

An electric current represents electric charges flowing through a conductor. By tradition, the current is modeled as a flow of positive charges, even though it was later discovered that current is in fact a flow of negative charges. The ampere, or amp, is the unit for the current, and is determined by the rate of flow of the charges. 1 amp is equal to 1 coulomb per second.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1A=\frac{1C}{1s}}

or

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle i(t)=\frac{dq}{dt}}

Since current is the rate of charge flowing through a certain cross section of conductor, we can get the total charge that has flowed through the same cross section over a period of time by integrating the current over time.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q(t)=\int_{t_0}^{t} i(t) dt}

Power (Watt)

The power absorbed or produced by a component is the rate at which it expends or generates energy. The unit for power is the watt, and 1 watt is equal to 1 joule per second. Written in terms of voltage and current, the power is equal to the voltage across the component multiplied by the current through the component. Thus, we get:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle P=IV\,}

If we check the units for the equation above, we get:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle W=\frac{C}{s} \cdot \frac{J}{C}=\frac{J}{s}}

Capacitance (Farad)

The unit of measurement for the capacitance of a capacitor is the farad, which is equal to 1 coulomb per volt.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1F=\frac{1C}{1V}}

Mechanical Analogues for Resistors, Capacitors, and Inductors

Symbols, Variables, and Units

	symbol	variable	units
current source	File:Current source symbol.jpg	I	Ampere (A)
voltage source	File:Voltage source round symbol.jpg or File:Voltage source batt symbol.jpg	V	Volt (V)
resistor	File:Resistor symbol.jpg	R	Ohm (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Omega} )
capacitor	File:Capacitor symbol.jpg or File:Capacitor polarized symbol.jpg (polarized)	C	Farad (F)
Inductor	File:Inductor symbol.jpg	L	Henry (H)