Chapter 18Parallel Circuits

Kirchhoff’s Rules

So, what happens after the battery is connected to this circuit?

The current divides, with part of it going through R1 and part of it going through R2.

V R2

+

_R1

The voltage across R1 and R2 must be the same!

I

I1

I2

Just like capacitors in parallel!

How does the currentdivide?

Let’s again resort to a classical analogy.

I1 I2

I

I

I1 I2

I

I

How will I1 and I2 compare if drain 1 is cloggedwith a LOT of leaves while I just cleaned drain 2last weekend?

I2 > I1

The water will take the path of least resistance!

I1 I2

I

I

Notice that the current divides at the corner ofthe roof, then recombines before heading tothe storm sewer.

I = I1 + I2

Let’s now return to our electrical circuit...

We can construct an equivalent circuit with a single resistor...

V R2

+

_R1

I

I1

I2

V Req

+

_I

V = I1R1 = I2R2 I = I1 + I2

conservation of charge

V = I Req

Resistors in parallel ADD INVERSELY.

1 1 1 = + Req R1 R2

V Req

+

_I

V = I1R1 = I2R2

I1 = V / R1

I2 = V / R2

I = V / Req

V VI = I1 + I2 = + R1 R2

V V V = + Req R1 R2

Req < R1, R2...

The current flowing through a circuitwith resistors connected in parallel willbe much greater than the current throughthe series circuit.

This is why it is NOT a good idea to plugtoo many appliances into the same electricaloutlet! Eventually, the breaker will trip!

Resistors in series simply add.

Capacitors in parallel simply add.

Resistors in parallel add inversely.

Capacitors in series add inversely.

V R2

+

_R1

I

I1

I2

junctionpoints

Junction points are places in the circuitwhere the current splits or rejoins.

You will only find junction points in parallelcircuits. You can use them to identify theparts of a more complicated circuit thatare wired in parallel.

We use parallel circuits to wire our houses,offices, dorm rooms, etc., etc., etc.

In a parallel circuit, eachoutlet gets the samevoltage.

If one element in thecircuit fails, the otherswill continue to receivecurrent.

Why do we want our outlets wired in parallel?

BreakerBox

Outlets with Appliances

Current flows

Unlike in the series circuit, the failure of oneelement in the parallel circuit does not disablethe entire circuit.

2

2

10

5

3

What is the equivalent resistance of thiscombination of resistors?

2

2

10

5

3

2Req13

1 1

5

1

10

1

2

8

10Req1

Req1 = 1.25

21.25 3

Req

Req = 3 + 1.25 + 2

Req = 6.25

1) The sum of the currents entering a junction must equal the sum of currents leaving a junction. (Conservation of Charge)

2) The sum of potential differences across all the elements on any closed loop in a circuit must be zero. (Conservation of Energy)

Junction Rule

Loop Rule