Jan. 12 – Transformers

Watch this:

As you're watching it, remember that the bulbs are NOT plugged into anything!  The current through them is completely induced by the giant coil under them.

Formative assessment: can you predict the direction of the current through this wire if it is moving up through the magnetic field?

Answer: use the right hand rule to find the current goes into the page.

The final topic for this unit and the term is transformers!

Transformers!

Transfer electric energy from one circuit into another.

 - Use Faraday’s Law of Induction

 - Consists of an iron core and two coils of wire from different circuits.

 - A changing current (AC) in on coil creates a changing magnetic field in the core.  This induces a current in the second coil.

This can be used to increase or decrease the potential difference in the second coil “transforming the voltage.”

step-up transformer increases voltage,  V2 > V1

step-down transformer decreases voltage, V2 < V1

Energy cannot be created or destroyed.  

Therefore power is constant.

        P1 = P2
   I1 V1 = I2 V2
V1 / V2 = I2 / I1

where the 1 and 2 refer to the first or second loop.

The number of coils determines what V2 will be.

Let N1 and N2 be the number of coils on each side.

N1 / N2 = V1 / V2

How is this useful?

Ex) A power plant produces 4.0 MW of power at 2.2 x 10^4 V and is transmitted over 950 km.

a) How much power is loss in the transmission wire if the resistance along the power line is 0.054 Ω / km.

Answer:

I = P/V = 182 A

Power loss = I² R

                   = (182 A)²(0.054 Ω/km) (950 km)

                   = 1.70 x 10^6 W

b) If the plant steps-up the voltage to 500 kV, how much power is lost?

Answer:

must solve for I2….  

I2 = (V1 / V2)*I1

I2 = 8.01 A

Power loss = I² R

                   = (8.01 A)²(0.054 Ω/km) (950 km)

                   = 3.29 x10^3 W

Less power is loss if the voltage is stepped up.

Long range power lines have high V and small I.

Once it reaches the consumer, another transformer steps-down the potential to make it useful (120 V).

That's it!

Homework

• Continue working on homework from the Unit Outline.
• Mini-test is Thursday, Jan. 15.
• Continue working on our speaker project (Due Monday, Jan. 19).