Physics worksheet featuring ten practice problems on calculating voltage and turns ratios for step-up and step-down transformers.
Transformers physics worksheet with 10 calculation problems and answers.
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Step-by-step solution for: Transformers-Worksheet
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Show Answer Key & Explanations
Step-by-step solution for: Transformers-Worksheet
Let's solve each problem on the Transformers Worksheet using the GUFSSA method, which stands for:
- Given: List the known values
- Unknown: Identify what you're solving for
- Formula: Write the appropriate formula
- Substitute: Plug in the values
- Solve: Calculate the answer
- Answer: Box or state the final answer
We'll use the transformer equation:
$$
\frac{V_P}{V_S} = \frac{N_P}{N_S}
$$
Where:
- $ V_P $ = Primary voltage
- $ V_S $ = Secondary voltage
- $ N_P $ = Number of turns in primary
- $ N_S $ = Number of turns in secondary
---
Given:
- $ N_P = 2680 $ turns
- $ V_P = 5850 $ V
- $ V_S = 120 $ V
Unknown: $ N_S = ? $
Formula:
$$
\frac{V_P}{V_S} = \frac{N_P}{N_S} \Rightarrow N_S = N_P \cdot \frac{V_S}{V_P}
$$
Substitute:
$$
N_S = 2680 \cdot \frac{120}{5850}
$$
Solve:
$$
N_S = 2680 \cdot 0.0205128 \approx 55.0
$$
Answer: $ \boxed{55} $ turns ✔
---
Given:
- $ V_P = 12 $ V
- $ V_S = 2 \times 10^4 $ V = 20,000 V
- $ N_P = 21 $ turns
Unknown: $ N_S = ? $
Formula:
$$
\frac{V_P}{V_S} = \frac{N_P}{N_S} \Rightarrow N_S = N_P \cdot \frac{V_S}{V_P}
$$
Substitute:
$$
N_S = 21 \cdot \frac{20,000}{12} = 21 \cdot 1666.67 \approx 35,000
$$
Answer: $ \boxed{3.5 \times 10^4} $ turns ✔
---
Given:
- $ V_S = 119,340 $ V
- $ V_P = 117 $ V
- $ N_S = 25,500 $ turns
Unknown: $ N_P = ? $
Formula:
$$
\frac{V_P}{V_S} = \frac{N_P}{N_S} \Rightarrow N_P = N_S \cdot \frac{V_P}{V_S}
$$
Substitute:
$$
N_P = 25,500 \cdot \frac{117}{119,340} = 25,500 \cdot 0.000979 \approx 24.9
$$
Answer: $ \boxed{25} $ turns ✔
---
Given:
- $ N_S = 525 $ turns
- $ N_P = 12,500 $ turns
- $ V_P = 3510 $ V
Unknown: $ V_S = ? $
Formula:
$$
\frac{V_P}{V_S} = \frac{N_P}{N_S} \Rightarrow V_S = V_P \cdot \frac{N_S}{N_P}
$$
Substitute:
$$
V_S = 3510 \cdot \frac{525}{12,500} = 3510 \cdot 0.042 = 147.42
$$
Answer: $ \boxed{147} $ V ✔
---
Given:
- $ V_P = 120 $ V
- $ N_P = 75 $ turns
- $ N_S = 1500 $ turns
Unknown: $ V_S = ? $
Formula:
$$
\frac{V_P}{V_S} = \frac{N_P}{N_S} \Rightarrow V_S = V_P \cdot \frac{N_S}{N_P}
$$
Substitute:
$$
V_S = 120 \cdot \frac{1500}{75} = 120 \cdot 20 = 2400
$$
Answer: $ \boxed{2400} $ V ✔
---
Given:
- $ N_P = 1400 $ turns
- $ N_S = 140 $ turns
- $ V_S = 6.9 \times 10^4 $ V = 69,000 V
Unknown: $ V_P = ? $
Formula:
$$
\frac{V_P}{V_S} = \frac{N_P}{N_S} \Rightarrow V_P = V_S \cdot \frac{N_P}{N_S}
$$
Substitute:
$$
V_P = 69,000 \cdot \frac{1400}{140} = 69,000 \cdot 10 = 690,000
$$
Answer: $ \boxed{6.9 \times 10^5} $ V ✔
(Note: The answer key says $ 6.9 \times 10^4 $, but that’s incorrect — it should be $ 6.9 \times 10^5 $ V)
Wait! Let's double-check:
If $ V_S = 6.9 \times 10^4 = 69,000 $ V, and $ N_P/N_S = 10 $, then $ V_P = 10 \times 69,000 = 690,000 = 6.9 \times 10^5 $ V.
So the answer key is wrong here. It says $ 6.9 \times 10^4 $, but correct is $ \boxed{6.9 \times 10^5} $ V.
But let's re-read: "What is the voltage across the primary if the secondary voltage is $ 6.9 \times 10^4 $ V?"
Yes, so $ V_P = V_S \cdot \frac{N_P}{N_S} = 69,000 \cdot 10 = 690,000 $ V → $ \boxed{6.9 \times 10^5} $ V
✔ Corrected: Answer is $ \boxed{6.9 \times 10^5} $ V
---
Given:
- $ V_P = 120 $ V
- $ V_S = 12 $ V
- $ N_P = 500 $ turns
Unknown: $ N_S = ? $
Formula:
$$
N_S = N_P \cdot \frac{V_S}{V_P}
$$
Substitute:
$$
N_S = 500 \cdot \frac{12}{120} = 500 \cdot 0.1 = 50
$$
Answer: $ \boxed{50} $ turns ✔
---
Given:
- $ V_P = 120 $ V
- $ V_S = 6 $ V
- $ N_P = 240 $ turns
Unknown: $ N_S = ? $
Formula:
$$
N_S = N_P \cdot \frac{V_S}{V_P}
$$
Substitute:
$$
N_S = 240 \cdot \frac{6}{120} = 240 \cdot 0.05 = 12
$$
Answer: $ \boxed{12} $ turns ✔
---
Given:
- $ N_P = 1440 $ turns
- $ N_S = 60 $ turns
- $ V_P = 120 $ V
Unknown: $ V_S = ? $
Formula:
$$
V_S = V_P \cdot \frac{N_S}{N_P}
$$
Substitute:
$$
V_S = 120 \cdot \frac{60}{1440} = 120 \cdot 0.04167 = 5
$$
Answer: $ \boxed{5} $ V ✔
---
Given:
- $ N_P = 3120 $ turns
- $ N_S = 507 $ turns
- $ V_P = 120 $ V
Unknown: $ V_S = ? $
Formula:
$$
V_S = V_P \cdot \frac{N_S}{N_P}
$$
Substitute:
$$
V_S = 120 \cdot \frac{507}{3120} = 120 \cdot 0.1625 = 19.5
$$
Answer: $ \boxed{19.5} $ V ✔
---
| Problem | Answer |
|--------|--------|
| 1 | 55 turns |
| 2 | $ 3.5 \times 10^4 $ turns |
| 3 | 25 turns |
| 4 | 147 V |
| 5 | 2400 V |
| 6 | $ \boxed{6.9 \times 10^5} $ V *(Answer key has error)* |
| 7 | 50 turns |
| 8 | 12 turns |
| 9 | 5 V |
| 10 | 19.5 V |
> ⚠️ Note: Problem #6 in the answer key says $ 6.9 \times 10^4 $ V, but based on calculations, it should be $ 6.9 \times 10^5 $ V. Likely a typo in the key.
Let me know if you'd like this formatted as a printable solution sheet!
- Given: List the known values
- Unknown: Identify what you're solving for
- Formula: Write the appropriate formula
- Substitute: Plug in the values
- Solve: Calculate the answer
- Answer: Box or state the final answer
We'll use the transformer equation:
$$
\frac{V_P}{V_S} = \frac{N_P}{N_S}
$$
Where:
- $ V_P $ = Primary voltage
- $ V_S $ = Secondary voltage
- $ N_P $ = Number of turns in primary
- $ N_S $ = Number of turns in secondary
---
1. Step-down transformer
Given:
- $ N_P = 2680 $ turns
- $ V_P = 5850 $ V
- $ V_S = 120 $ V
Unknown: $ N_S = ? $
Formula:
$$
\frac{V_P}{V_S} = \frac{N_P}{N_S} \Rightarrow N_S = N_P \cdot \frac{V_S}{V_P}
$$
Substitute:
$$
N_S = 2680 \cdot \frac{120}{5850}
$$
Solve:
$$
N_S = 2680 \cdot 0.0205128 \approx 55.0
$$
Answer: $ \boxed{55} $ turns ✔
---
2. Step-up transformer (automobile)
Given:
- $ V_P = 12 $ V
- $ V_S = 2 \times 10^4 $ V = 20,000 V
- $ N_P = 21 $ turns
Unknown: $ N_S = ? $
Formula:
$$
\frac{V_P}{V_S} = \frac{N_P}{N_S} \Rightarrow N_S = N_P \cdot \frac{V_S}{V_P}
$$
Substitute:
$$
N_S = 21 \cdot \frac{20,000}{12} = 21 \cdot 1666.67 \approx 35,000
$$
Answer: $ \boxed{3.5 \times 10^4} $ turns ✔
---
3. Step-up transformer (electric power)
Given:
- $ V_S = 119,340 $ V
- $ V_P = 117 $ V
- $ N_S = 25,500 $ turns
Unknown: $ N_P = ? $
Formula:
$$
\frac{V_P}{V_S} = \frac{N_P}{N_S} \Rightarrow N_P = N_S \cdot \frac{V_P}{V_S}
$$
Substitute:
$$
N_P = 25,500 \cdot \frac{117}{119,340} = 25,500 \cdot 0.000979 \approx 24.9
$$
Answer: $ \boxed{25} $ turns ✔
---
4. Step-down transformer
Given:
- $ N_S = 525 $ turns
- $ N_P = 12,500 $ turns
- $ V_P = 3510 $ V
Unknown: $ V_S = ? $
Formula:
$$
\frac{V_P}{V_S} = \frac{N_P}{N_S} \Rightarrow V_S = V_P \cdot \frac{N_S}{N_P}
$$
Substitute:
$$
V_S = 3510 \cdot \frac{525}{12,500} = 3510 \cdot 0.042 = 147.42
$$
Answer: $ \boxed{147} $ V ✔
---
5. Step-up transformer (120 V line)
Given:
- $ V_P = 120 $ V
- $ N_P = 75 $ turns
- $ N_S = 1500 $ turns
Unknown: $ V_S = ? $
Formula:
$$
\frac{V_P}{V_S} = \frac{N_P}{N_S} \Rightarrow V_S = V_P \cdot \frac{N_S}{N_P}
$$
Substitute:
$$
V_S = 120 \cdot \frac{1500}{75} = 120 \cdot 20 = 2400
$$
Answer: $ \boxed{2400} $ V ✔
---
6. Transformer with given voltages and turns
Given:
- $ N_P = 1400 $ turns
- $ N_S = 140 $ turns
- $ V_S = 6.9 \times 10^4 $ V = 69,000 V
Unknown: $ V_P = ? $
Formula:
$$
\frac{V_P}{V_S} = \frac{N_P}{N_S} \Rightarrow V_P = V_S \cdot \frac{N_P}{N_S}
$$
Substitute:
$$
V_P = 69,000 \cdot \frac{1400}{140} = 69,000 \cdot 10 = 690,000
$$
Answer: $ \boxed{6.9 \times 10^5} $ V ✔
(Note: The answer key says $ 6.9 \times 10^4 $, but that’s incorrect — it should be $ 6.9 \times 10^5 $ V)
Wait! Let's double-check:
If $ V_S = 6.9 \times 10^4 = 69,000 $ V, and $ N_P/N_S = 10 $, then $ V_P = 10 \times 69,000 = 690,000 = 6.9 \times 10^5 $ V.
So the answer key is wrong here. It says $ 6.9 \times 10^4 $, but correct is $ \boxed{6.9 \times 10^5} $ V.
But let's re-read: "What is the voltage across the primary if the secondary voltage is $ 6.9 \times 10^4 $ V?"
Yes, so $ V_P = V_S \cdot \frac{N_P}{N_S} = 69,000 \cdot 10 = 690,000 $ V → $ \boxed{6.9 \times 10^5} $ V
✔ Corrected: Answer is $ \boxed{6.9 \times 10^5} $ V
---
7. Electric doorbell (12 V)
Given:
- $ V_P = 120 $ V
- $ V_S = 12 $ V
- $ N_P = 500 $ turns
Unknown: $ N_S = ? $
Formula:
$$
N_S = N_P \cdot \frac{V_S}{V_P}
$$
Substitute:
$$
N_S = 500 \cdot \frac{12}{120} = 500 \cdot 0.1 = 50
$$
Answer: $ \boxed{50} $ turns ✔
---
8. Model electric train (6 V)
Given:
- $ V_P = 120 $ V
- $ V_S = 6 $ V
- $ N_P = 240 $ turns
Unknown: $ N_S = ? $
Formula:
$$
N_S = N_P \cdot \frac{V_S}{V_P}
$$
Substitute:
$$
N_S = 240 \cdot \frac{6}{120} = 240 \cdot 0.05 = 12
$$
Answer: $ \boxed{12} $ turns ✔
---
9. Cell phone charger
Given:
- $ N_P = 1440 $ turns
- $ N_S = 60 $ turns
- $ V_P = 120 $ V
Unknown: $ V_S = ? $
Formula:
$$
V_S = V_P \cdot \frac{N_S}{N_P}
$$
Substitute:
$$
V_S = 120 \cdot \frac{60}{1440} = 120 \cdot 0.04167 = 5
$$
Answer: $ \boxed{5} $ V ✔
---
10. Laptop battery charger
Given:
- $ N_P = 3120 $ turns
- $ N_S = 507 $ turns
- $ V_P = 120 $ V
Unknown: $ V_S = ? $
Formula:
$$
V_S = V_P \cdot \frac{N_S}{N_P}
$$
Substitute:
$$
V_S = 120 \cdot \frac{507}{3120} = 120 \cdot 0.1625 = 19.5
$$
Answer: $ \boxed{19.5} $ V ✔
---
✔ Summary of Answers:
| Problem | Answer |
|--------|--------|
| 1 | 55 turns |
| 2 | $ 3.5 \times 10^4 $ turns |
| 3 | 25 turns |
| 4 | 147 V |
| 5 | 2400 V |
| 6 | $ \boxed{6.9 \times 10^5} $ V *(Answer key has error)* |
| 7 | 50 turns |
| 8 | 12 turns |
| 9 | 5 V |
| 10 | 19.5 V |
> ⚠️ Note: Problem #6 in the answer key says $ 6.9 \times 10^4 $ V, but based on calculations, it should be $ 6.9 \times 10^5 $ V. Likely a typo in the key.
Let me know if you'd like this formatted as a printable solution sheet!
Parent Tip: Review the logic above to help your child master the concept of transformer worksheet.
