An educational worksheet designed to help students practice calculating voltage, current, and power ratios in electrical transformers.

Let's solve the transformer problems step by step using the principles of transformers and the given formulas:

Given Formulas:

- $ \frac{V_1}{V_2} = \frac{n_1}{n_2} $
- $ V = IR $
- $ n_1 I_1 = n_2 I_2 $
- $ P = IV $

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## Problem 1:

We are given:
- Primary voltage $ V_1 = 120 \, \text{V} $
- Primary turns $ n_1 = 30 $
- Secondary turns $ n_2 = 600 $
- Primary current $ I_1 = 20 \, \text{A} $

We need to fill in the chart and determine if it's a step-up or step-down transformer.

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Step 1: Determine if it's step-up or step-down

Since $ n_2 > n_1 $ (600 > 30), this is a step-up transformer.

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Step 2: Find secondary voltage $ V_2 $

Using:
$$
\frac{V_1}{V_2} = \frac{n_1}{n_2}
\Rightarrow V_2 = V_1 \times \frac{n_2}{n_1}
= 120 \times \frac{600}{30} = 120 \times 20 = 2400 \, \text{V}
$$

So, $ V_2 = 2400 \, \text{V} $

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Step 3: Find secondary current $ I_2 $

Use power conservation (assuming ideal transformer first):

$$
P_{\text{in}} = P_{\text{out}} \Rightarrow V_1 I_1 = V_2 I_2
\Rightarrow I_2 = \frac{V_1 I_1}{V_2} = \frac{120 \times 20}{2400} = \frac{2400}{2400} = 1 \, \text{A}
$$

Alternatively, use:
$$
n_1 I_1 = n_2 I_2 \Rightarrow I_2 = \frac{n_1 I_1}{n_2} = \frac{30 \times 20}{600} = \frac{600}{600} = 1 \, \text{A}
$$

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Step 4: Power

Power input:
$$
P_{\text{in}} = V_1 I_1 = 120 \times 20 = 2400 \, \text{W}
$$

Assuming ideal (no losses), output power = input power = 2400 W

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Fill in the Chart for Problem 1:

| Step up or step down? | Primary | Secondary |
|------------------------|---------------|---------------|
| Voltage | 120 V | 2400 V |
| Current | 20 A | 1 A |
| # of Coils | 30 | 600 |
| Power | 2400 W | 2400 W |

✔ Answer: This is a step-up transformer.

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Problem 2: What is the output voltage if efficiency is only 75%?

> Important Note: Efficiency affects power, not voltage directly. The voltage ratio depends only on turns ratio (ideal transformer assumption). But real transformers have losses.

However, the question asks: *"What is the output voltage if it is only 75% efficient?"*

But efficiency does not change the voltage ratio unless specified otherwise. Voltage is determined by turns ratio.

So:
$$
V_2 = V_1 \times \frac{n_2}{n_1} = 120 \times \frac{600}{30} = 2400 \, \text{V}
$$

This remains unchanged.

But output power is reduced due to efficiency.

Efficiency $ \eta = \frac{P_{\text{out}}}{P_{\text{in}}} = 0.75 $

So:
$$
P_{\text{out}} = 0.75 \times 2400 = 1800 \, \text{W}
$$

Now, since $ P_{\text{out}} = V_2 I_2 $, we can find $ I_2 $:
$$
I_2 = \frac{P_{\text{out}}}{V_2} = \frac{1800}{2400} = 0.75 \, \text{A}
$$

But voltage remains 2400 V because it's determined by turns ratio.

> ✔ So, output voltage is still 2400 V — efficiency affects power and current, not voltage in ideal transformer models.

Unless there’s a load-dependent drop, but in basic problems like this, we assume voltage is fixed by turns ratio.

So answer to Q2:
Output voltage = 2400 V (unchanged)

---

Problem 3:

Given:
- $ n_1 = 200 $
- $ n_2 = 2000 $
- $ V_1 = 120 \, \text{V} $
- $ P_{\text{in}} = 1800 \, \text{W} $

We are to find output voltage and complete the table.

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Step 1: Is it step-up or step-down?

$ n_2 > n_1 $ → Step-up

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Step 2: Output voltage $ V_2 $

$$
\frac{V_1}{V_2} = \frac{n_1}{n_2} \Rightarrow V_2 = V_1 \times \frac{n_2}{n_1} = 120 \times \frac{2000}{200} = 120 \times 10 = 1200 \, \text{V}
$$

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Step 3: Input current $ I_1 $

$ P_{\text{in}} = V_1 I_1 \Rightarrow I_1 = \frac{P_{\text{in}}}{V_1} = \frac{1800}{120} = 15 \, \text{A} $

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Step 4: Output current $ I_2 $

Using power conservation (assume ideal transformer):

$$
P_{\text{out}} = P_{\text{in}} = 1800 \, \text{W}
\Rightarrow I_2 = \frac{P_{\text{out}}}{V_2} = \frac{1800}{1200} = 1.5 \, \text{A}
$$

Or use:
$$
n_1 I_1 = n_2 I_2 \Rightarrow I_2 = \frac{n_1 I_1}{n_2} = \frac{200 \times 15}{2000} = \frac{3000}{2000} = 1.5 \, \text{A}
$$

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Step 5: Power

Input and output power both = 1800 W (ideal case)

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Fill in the Chart for Problem 3:

| Step up or step down? | Primary | Secondary |
|------------------------|---------------|---------------|
| Voltage | 120 V | 1200 V |
| Current | 15 A | 1.5 A |
| # of Coils | 200 | 2000 |
| Power | 1800 W | 1800 W |

✔ Answer: This is a step-up transformer.

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## ✔ Final Answers:

Problem 1:

- Step-up transformer
- Chart filled as above.

Problem 2:

- Output voltage is 2400 V even at 75% efficiency.
- (Note: Efficiency affects power, not voltage in standard model.)

Problem 3:

- Step-up transformer
- Output voltage = 1200 V
- Chart filled as above.

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Let me know if you want a visual diagram or explanation of how efficiency would affect real-world transformers!