Transformers (Basics & Laws) (2)

Define a transformer.

An electromagnetic device that changes AC voltage and current levels (step up or down) via electromagnetic induction with minimal energy loss.

What is mutual induction vs. self-induction?

Mutual induction: varying current in one coil induces EMF in a second coil (standard transformer). Self-induction: EMF induced in the same coil (autotransformer).

How do step-up and step-down transformers change voltage and current?

Step-up: increases voltage and decreases current (Ns>Np). Step-down: decreases voltage and increases current (Ns<Np).

State the transformer law for voltage.

Vs/Vp = Ns/Np (voltage change is directly proportional to the turns ratio).

State the transformer law for current.

Is/Ip = Np/Ns (current change is inversely proportional to the turns ratio).

What does conservation of power imply for an ideal transformer?

Power in ≈ power out: Vp·Ip ≈ Vs·Is (neglecting losses).

Calculate Vs for a step-up transformer with Vp=110 V and turns ratio Ns:Np=12:1.

Vs = 110 V × 12 = 1,320 V.

Calculate Is for a step-up transformer with Ip=38 A and Ns:Np = 12:1.

Is = Ip × (Np/Ns) = 38 A × (1/12) ≈ 3.17 A.

Given a step-down transformer with Ip=33 A and Is=79 A, what is Ns/Np and the voltage ratio?

Ns/Np = Ip/Is = 33/79 ≈ 0.418 (step-down). Thus Vs/Vp ≈ 0.418 (Vs = 0.418×Vp).

Express a turns ratio for a transformer factor of 0.8.

Turns ratio Ns:Np = 0.8:1 (step-down).

If Np=100 and Ns=350, what kind of transformer is it and what is the turns ratio?

Step-up transformer with Ns:Np = 350:100 = 3.5:1.

Use Ns/Np=125/25 and Vp=220 V to find Vs.

Ns/Np=5, so Vs = 220 V × 5 = 1,100 V.

Use Ns/Np=125/25 (5:1) and Ip=30 A to find Is.

Is = Ip × (Np/Ns) = 30 A × (1/5) = 6 A.

If Vp=165 V, Ip=36 A, and Vs=96 V, find Is.

Is ≈ (Vp·Ip)/Vs = (165×36)/96 = 61.875 A ≈ 61.9 A.

What does an autotransformer do and what principle does it use?

Provides adjustable voltage via a single coil that taps different turns; operates by self-induction.