materials that allow the free flow of electric charge within them (metals)
the flow of charge between two points at different electric potentials connected by a conductor
Equation to determine the total electric current passing through a conductor per unit of time:
I = Δq/Δt
where Δq is the amount of charge and Δt is time
The SI unit of current:
ampere (1 A = 1 coulomb/second)
The direction of current is:
the direction in which positive charge would flow from higher potential to lower potential. The direction of current is opposite the direction of actual electron flow.
The two patterns of current flow:
Direct current (DC; flows in one direction) and alternating current (AC; flow changes direction periodically)
the potential difference (voltage) between two terminals of a cell at different potentials when there is no charge moving; a "pressure to move" that results in current
Kirchoff's Junction Rule:
at any point or junction in a circuit, the sum of the currents directed into that point equals the sum of the currents directed away from that point.
Circuits and currents are governed by:
the laws of the conservation of energy; charge and energy can be neither created or destroyed
Kirchoff's Loop Rule:
Around any closed circuit loop, the sum of the voltage sources will always be equal to the sum of voltage (potential) drops.
the opposition to the movement of electrons through a material
Materials with low resistance:
Materials with very high resistance that essentially stop the flow of electrons:
Conductive materials with a moderate amount of resistance, which slows down electrons without stopping them:
Equation to determine the resistance of a given resistor:
R = pL/A
where p is the resistivity, R is the resistance, L is the length of the resistor, and A is the cross-sectional area of the resistor
SI unit of resistance:
The longer the length of the resistor:
the greater the resistance
The larger the cross-sectional area of a resistor:
the less the resistance
The higher the temperature of a resistor:
the greater the resistance (due to increased thermal oscillation of the atoms in the conductive material)
The 4 major factors that contribute to resistance:
3) cross-sectional area
Equation used to determine the drop in electric potential across a resistor:
V = iR
where V is the voltage drop, i is the current, and R is the magnitude of resistance
Equation to determine the actual voltage supplied by a cell to a circuit:
V = εcell - irint
where i is the current, rint is the internal resistance of the material, and εcell is the emf of the cell
Equation to determine power:
P = E/Δt
where E is energy and t is time
Equation to determine the power dissipated by a resistor:
P = iV = i2R = V2/R
where i is the current through the resistor, V is the voltage drop across the resistor, and R is the resistance of the resistor
The two ways resistors can be connected in a circuit:
in a series or parallel
Voltage drops through a series of resistors are:
Vs = V1 + V2 + V3 + V4 + ...
In a circuit with a series of resistors, the current is:
the same at every point in the circuit, including through every resistor
Equation to determine the total voltage drop across multiple resistors in a series:
Vs = V1 + V2 + V3 + V4 + ...
Equation to determine the resultant resistance of multiple resistors in a series:
Rs = R1 + R2 + R3 + R4 + ...
When resistors are connected in parallel, they are wired with:
a common high-potential terminal and a common low-potential terminal
Equation to determine the total voltage drop across multiple resistors in parallel:
Vp = V1 = V2 = V3 = V4 ...
Equation to determine the resultant resistance of multiple resistors in parallel:
1/Rp = 1/R1 + 1/R2 + 1/R3 + ...
When n identical resistors are wired in parallel, the total resistance is given by the equation:
When approaching circuit problems, the first three things you need to find are:
1) total voltage
2) total resistance
3) total current
Ohm's law states that:
for a given resistance, the magnitude of the current through a resistor is proportional to the voltage drop across the resistor
Across each resistor in a circuit, a certain amount of ___ is dissipated.
The amount of power dissipated by a resistor in a circuit is dependent on:
the current through the resistor and the voltage drop across the resistor
Resistors in series are:
additive and sum together to create the total resistance of the circuit
Resistors in parallel:
cause a decrease in resultant resistance of a circuit
Equation to determine the capacitance of a capacitor:
C = Q/V
where Q is the absolute value of the charge and V is the voltage applied
SI unit of capacitance:
(1F = 1 coulomb/volt)
microfarads (uF) =
1 X 10-6 F
picofarads (pF) =
1 X 10-12F
Equation to determine the capacitance of a parallel plate capacitor:
C = εo (A/d)
where εo is 8.85 X 10-12, A is the area of overlap of the two plates, and d is the separation of the two plates
Equation to determine the electric field at a point in space between the plates of a parallel plate capacitor:
E = V/d
where V is the volatage applied across the plates and d is the separation between the plates
The direction of the electric field at any point between parallel plate capacitors is:
away from the positive plate and toward the negative plate
Equation to determine the potential energy stored in a capacitor:
U = 1/2CV2
where C is the capacitance of the capacitor and V is the voltage applied
A dielectric material is:
an insulator placed between the plates of a capacitor that increases the capacitance of the capacitor by a factor equal to the material's dielectric constant, K
Dielectric constant (K) is:
a measure of the insulating capability of a particular dielectric material
Equation used to determine the increase in capacitance due to a dielectric material:
C' = KC
where C' is the new capacitance and C is the original capacitance
Capacitance of capacitors in series behave in the same manner as:
resistors in parallel
Equation to determine the total voltage across multiple capacitors in series:
Vs = V1 + V2 + V3 + V4 + ...
Equation to determine the resultant capacitance across multiple capacitors in series:
1/Cs = 1/C1 + 1/C2 + 1/C3 + ..
Adding resistors in parallel ___ overall resistance:
Adding capacitors in parallel ___ overall capacitance:
Equation to determine the total voltage across multiple capacitors in parallel:
Vp = V1 = V2 = V3 = V4 + ...
Equation to determine the resultant capacitance across multiple capacitors in parallel:
Cp = C1 + C2 + C3 + C4 + ...
In series, what happens to the capacitance as more capacitors are added?
In parallel, what happens to the capacitance as more capacitors are added?
The equations for voltage, resistance, and capacitance in series:
Vs = V1 + V2 + V3 ...
Rs = R1 + R2 + R3 ...
1/Cs = 1/C1 + 1/C2 + 1/C3
The equations for voltage, resistance, and capacitance in parallel:
Vp = V1 = V2 = V3 ...
1/Rp = 1/R1 + 1/R2 + 1/R3 ...
Cp = C1 + C2 + C3 + ...
Alternating current oscillates in what manner?
sinusoidal, from +imax to -imax
Equation to estimate the average magnitude of alternating current over time:
irms = imax / √2
where imax is the maximum current and irms is the average current
Capacitors have the ability to:
store electric charge and discharge the energy later
Equation to estimate the average magnitude of AC voltage over one period:
Vrms = Vmax / √2
where Vmax is the maximum voltage and Vrms is the average voltage
Once you have calculated the Irms and Vrms values for alternating current, what can you plug these values into?
Equation for the instantaneous current of an alternating current:
i = imaxsin(2πft) = imaxsin(ωt)
where i is the instantaneous current, imax is the maximum current, f is the frequency, and ω is the angular frequency