SME
Grade 11 Science · Problem type
A transformer
Use this for “A transformer steps 120 V down with 400 primary turns and 20 secondary turns. What voltage comes out, and what current if 0.1 A goes in?”
Diagram
Vₛ
=
Vₚ
×
Nₛ/Nₚ
=
120
×
20
400
Vₛ = 6 V
Iₛ = Iₚ × Nₚ/Nₛ = 0.1 × 400/20 = 2 A: VₚIₚ = VₛIₛ = 12 W, the power kept.
The alternating current in the primary makes a changing field in the iron, which induces the voltage in the secondary.
This is an example. Type your own values to start a new problem.
Vₛ (V)
Vₚ (V)
=
Nₛ
Nₚ
Iₚ
Primary current
example
Iₛ
Secondary current
calculated
Formulas
Vₛ = Vₚ × Nₛ/Nₚ
6
=
120
×
20
400
Iₛ = Iₚ × Nₚ/Nₛ
2
=
0.1
×
400
20
Assumptions
•
An alternating current makes a changing flux in the iron core, which induces a voltage in the secondary coil.
•
The voltage per turn is the same in both coils: Vₛ/Vₚ = Nₛ/Nₚ.
•
An ideal transformer keeps the power, VₚIₚ = VₛIₛ: stepping the voltage down steps the current up.
Step-by-step
WE KNOW
Nₚ = 400, Nₛ = 20, Vₚ = 120 V, Iₚ = 0.1 A
FIND
secondary voltage (Vₛ), secondary current (Iₛ)
Step 1 · Find secondary voltage (Vₛ)
Use Vₛ = Vₚ × Nₛ/Nₚ
The same voltage per turn: multiply by the turns ratio.
Vₛ
=
120
×
20
400
Vₛ = 6 V
Step 2 · Find secondary current (Iₛ)
Use Iₛ = Iₚ × Nₚ/Nₛ
Power kept: the current changes the other way from the voltage.
Iₛ
=
0.1
×
400
20
Iₛ = 2 A
Check
Put the numbers back in. Both sides should match.
6
=
120
×
20
400
✓
2
=
0.1
×
400
20
✓
Topic check
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