Parallel Circuits

Parallel Circuit- A parallel circuit is defined as one having more than one current path connected to a common voltage source. Parallel circuits, therefore, must contain two or more load resistances which are not connected in series.

Current in a Parallel Circuit: In electrical circuits it is important to understand how current works. In a parallel circuit current adds up, unlike a series circuit where current is constant.

Visual Ex.1- parallel circuit with one battery and two loads 3amps1.5amps 3amps 1.5amps

Visual Ex.2- parallel circuit with one load and two batteries 6v 1.5am ps 1.5amps1.5amps 1.5amps1.5amps =3amps 3amps 1.5amps1.5amps 1.5amps1.5amps 6v 3amps

Visual Ex. 3-Circuit with multiple loads Parallel Double Power Source 6v 3 amp 6v 3amp 3amps3amps 3 amps3+3=6 amps 3amps3amps Amps split at junction Junction: Point at which 2 wires meet 3amps3amps 3 amps Amps rejoin at junction 6 amps 3amps3amps 3amps3amps

Resistance in a Parallel Circuit Total Resistance: The total resistance of a circuit can be determined by substituting total values of voltage and current into Ohm’s law Ohms Law: R t = E t /I t where “t” represents total Total resistance (R t ) is also referred to as equivalent resistance (R eq ).

Resistance In parallel circuits the equivalent resistance will always be smaller than the resistance of any branch V = I x R If voltage is constant then a smaller R results in a higher I V = I x R

R eq = R/N where: R eq = Equivalent parallel resistance R = Ohmic value of one resistor N = Number of resistors Resistance: Resistors of Equal Values

Resistance: Resistors of unequal values Simplify: R t = 1 / (1/R 1 +1/R 2 +….1/R n )

Resistance example 1 R1 = 20 ohms R2 = 30 ohms R3 = 40 ohms Use the equation: R t = 1/(1R1+1/R2+….1/Rn) Substitute: R t = 1/(1/20+1/30+1/40) R t = 9.23 ohms 20Ω 9.23Ω 30Ω40Ω

Resistance example 2 Original CircuitEquivalent Circuit Req 12 ohms R1 20 ohms R2 30 ohms Example: R1 = 20 R2 = 30 Find Req = ? Equivalent resistance: Rt = 1/ (1/R1+1/R2) Rt = 1 / (1/20 + 1/30) Rt = 12 ohms

Parallel Power Source Characteristics in a Parallel Circuit Parallel Power supplies provide a higher current capacity. (amps add up) Yet the voltage stays the same throughout the circuit In parallel connection, all positive cell electrodes are connected to one line, and all negative electrodes are connected to one line. No more than one cell is connected between the lines at any one point. The only amps discharged from a battery are the amps required for a load. This occurs even though the battery is capable of outputting more.

In Conclusion: Rules for Solving Parallel D-C Circuits 1.The same voltage exists across each branch of a parallel circuit and is equal to the source voltage. 2.The total current of a parallel circuit is equal to the sum of the currents of the individual branches of the circuit. 3.The total resistance of a parallel circuit is equal to the reciprocal of the sum of the reciprocals of the individual resistances of the circuit.