Parallel CircuitsParallel Circuits

Parallel Circuit-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: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 Visual Ex.1- parallel circuit with one battery and two loads battery and two loads

3amps 1.5amps

1.5amps

1.5amps3amps

1.5amps

Visual Ex.2- parallel circuit with one Visual Ex.2- parallel circuit with one load and two batteries load and two batteries

6v

1.5amps

1.5 amps

1.5amps

1.5+1.5=3amps 3amps

3amps

1.5amps

1.5amps

6v

3amps

Visual Ex. 3-Circuit with multiple Visual Ex. 3-Circuit with multiple loadsloads

Parallel Double Power Source

6v

3 amp

6v

3amp3amps

3 amps 3+3=6 amps

3 amps

Amps split at junction

Junction: Point at which 2 wires meet

3amps

3 amps

Amps rejoin at junction6 amps

3amps

3amps

Resistance in a Parallel CircuitResistance 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: Rt = Et/It where “t” represents total

• Total resistance (Rt) is also referred to as equivalent resistance (Req) .

Resistance

• In parallel circuits the equivalent resistance will always be smaller than the resistance of any branch

V = I x RIf voltage is constant then a smaller R results in a higher I

V = I x R

Req = R/N where: Req = Equivalent parallel

resistanceR = Ohmic value of one resistorN = Number of resistors

Resistance: Resistors of Equal Values

Resistance: Resistors of unequal values

• Simplify: Rt = 1 / (1/R1+1/R2+….1/Rn)

Resistanceexample 1

• R1 = 20 ohms• R2 = 30 ohms• R3 = 40 ohms• Use the equation:

Rt = 1/(1R1+1/R2+….1/Rn)

• Substitute: Rt = 1/(1/20+1/30+1/40)

• Rt= 9.23 ohms

20Ω

9.23Ω

30Ω 40Ω

Resistanceexample 2

Original Circuit Equivalent Circuit

Req12 ohms

R120 ohms

R230 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 Parallel Power Source Characteristics in a Parallel CircuitCharacteristics 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:In Conclusion:Rules for Solving Parallel D-C CircuitsRules 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.