Parallel circuits Flashcards
branch
a parallel path in a circuit
parallel circuit (definition)
if there is more than one current path (branch) between two points, and if the voltage between those two points also appears across each of the branches, then there is a parallel circuit between those two points
resistors in parallel (formula)
πΊβ = πΊβ + πΊβ + β¦ + πΊβ
π β = 1/[(1/π β) + (1/π β) + β¦ + (1/π β)]
two resistors in parallel (formula)
π β = (π βπ β)/(π β + π β)
the total resistance for two resistors in parallel is equal to the product of the two resistors divided by the sum of the two resistors
equal-value resistors in parallel (formula)
π β = π /n
open parallel circuit
when one branch of a parallel circuit opens, the total resistance increases, the total current decreases, and the same current continues through each of the remaining parallel paths
voltage in a parallel circuit
voltage across each parallel resistor is the same, and each is equal to the source voltage
node
any point or junction in a circuit where two or more components are connected
Kirchoffβs current law
πΌin1 + πΌin2 + β¦ + πΌin(n) = πΌout1 + πΌout2 + β¦ + πΌout(n)
The sum of the currents into a node (total current in) is equal to the sum of the currents out of that node (total current out).
πΌin1 + πΌin2 + β¦ + πΌin(n) β πΌout1 β πΌout2 β β¦ β πΌout(n) = 0
The algebraic sum of all of the currents entering and leaving a node is equal to zero.
current in a parallel circuit
The total current divided among parallel resistors into currents with values inversely proportional to the resistance values.
branches with higher resistance have less current, and branches with lower resistance have more current, in accordance with Ohmβs law
current divider formula
πΌβ = (π β/π β)πΌβ
The current (πΌβ) through any branch equals the total parallel resistance (π β) divided by the resistance (π β) of that branch, and then multiplied by the total current (πΌβ) into the junction of parallel branches.
current divider formula for two branches
πΌβ = [π β/(π β + π β)]πΌβ
πΌβ = [π β/(π β + π β)]πΌβ
power formulas for parallel circuits
πβ = πΌβΒ²π β
πβ = πβπΌβ
πβ = πβΒ²/π β
πβ is the source voltage across the series circuit, π β is the total resistance, and πΌβ is the total current into the parallel circuit
power for resistors in parallel
πβ = πβ + πβ + β¦ + πβ
short in a parallel circuit
when a branch in a parallel circuit shorts, the current increases to an excessive value, usually causing the resistor to burn open or a fuse or circuit breaker to blow
