SME
Circuit Analysis II
Transformers
Use this for “A 10:1 transformer has 120 V on its primary and a 4 Ω load. Find the currents.”
Diagram
Vₛ
=
Vₚ
×
Nₛ/Nₚ
=
120
×
50
500
Vₛ = 12 V
Iₛ = Iₚ × Nₚ/Nₛ = 0.3 × 500/50 = 3 A: VₚIₚ = VₛIₛ = 36 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
Iₛ (A)
=
Vₛ (V)
RL (Ω)
Iₚ (A)
=
Iₛ (A)
×
Nₛ
Nₚ
Rᵢₙ
Input resistance
calculated
Formulas
Vₛ
=
Vₚ
×
Nₛ
Nₚ
12
=
120
×
50
500
Iₛ
=
Vₛ
RL
3
=
12
4
Iₚ
=
Iₛ
×
Nₛ
Nₚ
0.3
=
3
×
50
500
Rᵢₙ
=
(
Nₚ
Nₛ
)
2
×
RL
400
=
(
500
50
)
2
×
4
Assumptions
•
Ideal transformer: no losses, and all the flux in the core links both coils, so each turn carries the same voltage.
•
Power in equals power out, VₚIₚ = VₛIₛ: stepping the voltage down steps the current up.
•
Voltages and currents are rms values of one AC sine wave; the load is a resistor.
Step-by-step
WE KNOW
Nₚ = 500, Nₛ = 50, Vₚ = 120 V, RL = 4 Ω
FIND
secondary voltage (Vₛ), secondary current (Iₛ), primary current (Iₚ), input resistance (Rᵢₙ)
Step 1 · Find secondary voltage (Vₛ)
Use Vₛ = Vₚ × Nₛ ÷ Nₚ
Every turn carries the same voltage, so the voltage scales with the turns.
Vₛ
=
120
×
50
500
Vₛ
=
6,000
500
Vₛ = 12 V
Step 2 · Find secondary current (Iₛ)
Use Iₛ = Vₛ ÷ RL
Ohm’s law for the load across the secondary.
Iₛ
=
12
4
Iₛ = 3 A
Step 3 · Find primary current (Iₚ)
Use Iₚ = Iₛ × Nₛ ÷ Nₚ
Power in equals power out, so the current scales the opposite way to the voltage.
Iₚ
=
3
×
50
500
Iₚ
=
150
500
Iₚ = 0.3 A
Step 4 · Find input resistance (Rᵢₙ)
Use Rᵢₙ = (Nₚ ÷ Nₛ)² × RL
The
voltage
goes
up
by
the
turns
ratio
and
the
current
down
by
it,
so
Vₚ
Iₚ
is
the
ratio
squared
times
RL.
Rᵢₙ
=
(
500
50
)
2
×
4
Rᵢₙ
=
10
2
×
4
Rᵢₙ = 100 × 4
Rᵢₙ = 400 Ω
Check
Put the numbers back in. Both sides should match.
12
=
120
×
50
500
✓
3
=
12
4
✓
0.3
=
3
×
50
500
✓
400
=
(
500
50
)
2
×
4
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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