Chapter 18 Parallel Circuits Kirchhoff’s Rules

So, what happens after the battery is connected to this circuit? The current divides, with part of it going through R 1 and part of it going through R 2. V R2R2 + _ R1R1 The voltage across R 1 and R 2 must be the same! I I1I1 I2I2 Just like capacitors in parallel!

How does the current divide? Let’s again resort to a classical analogy. I1I1 I2I2 I I

I1I1 I2I2 I I How will I 1 and I 2 compare if drain 1 is clogged with a LOT of leaves while I just cleaned drain 2 last weekend? I 2 > I 1 The water will take the path of least resistance!

I1I1 I2I2 I I Notice that the current divides at the corner of the roof, then recombines before heading to the storm sewer. I = I 1 + I 2 Let’s now return to our electrical circuit...

We can construct an equivalent circuit with a single resistor... V R2R2 + _ R1R1 I I1I1 I2I2 V R eq + _ I V = I 1 R 1 = I 2 R 2 I = I 1 + I 2 conservation of charge V = I R eq

Resistors in parallel ADD INVERSELY = + R eq R 1 R 2 V R eq + _ I V = I 1 R 1 = I 2 R 2 I 1 = V / R 1 I 2 = V / R 2 I = V / R eq V V I = I 1 + I 2 = + R 1 R 2 V V V = + R eq R 1 R 2

R eq < R 1, R 2... The current flowing through a circuit with resistors connected in parallel will be much greater than the current through the series circuit. This is why it is NOT a good idea to plug too many appliances into the same electrical outlet! 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 R2R2 + _ R1R1 I I1I1 I2I2 junction points Junction points are places in the circuit where the current splits or rejoins. You will only find junction points in parallel circuits. You can use them to identify the parts of a more complicated circuit that are wired in parallel.

We use parallel circuits to wire our houses, offices, dorm rooms, etc., etc., etc. In a parallel circuit, each outlet gets the same voltage. If one element in the circuit fails, the others will continue to receive current.

Why do we want our outlets wired in parallel? Breaker Box Outlets with Appliances Current flows Unlike in the series circuit, the failure of one element in the parallel circuit does not disable the entire circuit.

22 22 10  55 33 What is the equivalent resistance of this combination of resistors?

22 22 10  55 33 22 R eq1 33 R eq1 = 1.25 

22 1.25  33 R eq R eq = 3   + 2  R eq = 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