Physics worksheet featuring transformer diagrams, formulas for voltage and current, and practice problems for calculating efficiency and output voltage.

Let's solve the Transformers Worksheet step by step, using the principles of transformers and the given formulas:

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Key Transformer Formulas:

1. Voltage Ratio:
$$
\frac{V_1}{V_2} = \frac{n_1}{n_2}
$$

2. Current Ratio (assuming ideal transformer):
$$
\frac{I_1}{I_2} = \frac{n_2}{n_1}
$$

3. Power Conservation (ideal):
$$
P_1 = P_2 \Rightarrow V_1 I_1 = V_2 I_2
$$

4. Efficiency:
$$
\text{Efficiency} = \frac{\text{Output Power}}{\text{Input Power}} \times 100\%
$$

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## Problem 1: Fill in the chart for the first transformer

Given:
- Primary voltage $ V_1 = 120 \, \text{V} $
- Primary current $ I_1 = 20 \, \text{amps} $
- Primary turns $ n_1 = 30 $
- Secondary turns $ n_2 = 600 $

We are to fill in the table:

| Step up or step down? | Primary | Secondary |
|------------------------|---------|-----------|
| Voltage | | |
| Current | | |
| # of Coils | | |
| Power | | |

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Step 1: Determine if it’s a step-up or step-down transformer

- $ n_1 = 30 $, $ n_2 = 600 $ → secondary has more turns → Step-up transformer

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Step 2: Find Secondary Voltage ($ V_2 $)

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

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Step 3: Find Secondary Current ($ I_2 $)

Using power conservation (ideal):
$$
P_1 = V_1 I_1 = 120 \cdot 20 = 2400 \, \text{W}
$$
$$
P_2 = V_2 I_2 \Rightarrow I_2 = \frac{P_2}{V_2} = \frac{2400}{2400} = 1 \, \text{A}
$$

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

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Step 4: Number of coils

- Primary: 30
- Secondary: 600

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Step 5: Power

- Ideal transformer: Power in = Power out
- $ P_1 = 120 \cdot 20 = 2400 \, \text{W} $
- $ P_2 = 2400 \cdot 1 = 2400 \, \text{W} $

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✔ Completed Table 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: Step-up transformer

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

Now, efficiency is 75%, so output power is only 75% of input power.

But voltage is determined by turns ratio, which depends on the physical design — voltage ratio remains the same unless the core or winding changes.

So:
- $ V_2 = 2400 \, \text{V} $ (same as before)
- But power output is reduced

Let’s compute:

- Input power $ P_{in} = 2400 \, \text{W} $
- Efficiency = 75%, so:
$$
P_{out} = 0.75 \times 2400 = 1800 \, \text{W}
$$
- Output voltage $ V_2 $ still comes from turns ratio: $ V_2 = 2400 \, \text{V} $
- So output current:
$$
I_2 = \frac{P_{out}}{V_2} = \frac{1800}{2400} = 0.75 \, \text{A}
$$

But the question asks: What is the output voltage?

➡️ Answer: The output voltage is still 2400 V.

> 🔍 Why? Because voltage is determined by the turns ratio and input voltage. Efficiency affects power and current, not voltage in an ideal transformer model (unless specified otherwise). In real transformers, voltage drop due to losses can occur, but here we assume the voltage ratio holds.

✔ Final Answer: Output voltage = 2400 V

> Note: Even at 75% efficiency, the voltage is still governed by the turns ratio.

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## Problem 3: New transformer with different turns

Given:
- $ n_1 = 200 $
- $ n_2 = 2000 $
- $ V_1 = 120 \, \text{V AC} $
- $ I_1 = 1800 \, \text{turns} $? Wait — this seems like a typo.

Wait: "runs at 1800 turns" — that doesn't make sense. Probably a mistake.

Let’s re-read:
> "The input voltage is 120 VAC, and runs at 1800 turns."

This is ambiguous. But earlier it says:
> "a primary coil with 200 turns, and a secondary coil with 2000 turns"

So likely, “runs at 1800 turns” is a typo or misstatement.

Possibility: Maybe it means primary current is 1800 amps? That would be huge — unrealistic.

Or maybe 1800 watts? Let's check context.

Wait — perhaps it's a typo and should say "draws 1800 watts"?

But let’s look carefully:

> "The input voltage is 120 VAC, and runs at 1800 turns."

That makes no sense — the number of turns is already given as 200.

Another possibility: "runs at 1800 watts"?

Let’s assume it's input power = 1800 W — because otherwise the statement is invalid.

But wait — perhaps it's "current"?

Let’s suppose it's a typo and meant to say:

> "and draws 1800 watts" → then we can proceed.

But the sentence says: "runs at 1800 turns" — which contradicts the given 200 turns.

Alternatively, could it be 1800 rpm? No — not relevant.

Wait — maybe "the primary current is 1800 A"? That’s extremely high for 120 V.

Let’s calculate what current would give 1800 W:

If $ P = V \cdot I $, then $ I = P / V $

Suppose $ P = 1800 \, \text{W} $, $ V = 120 \, \text{V} $ → $ I = 15 \, \text{A} $

So probably: "runs at 1800 watts" — typo for "watts".

Let’s assume that.

So corrected:
- $ n_1 = 200 $
- $ n_2 = 2000 $
- $ V_1 = 120 \, \text{V} $
- $ P_1 = 1800 \, \text{W} $

Then we can find everything.

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Step 1: Output Voltage ($ V_2 $)

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

→ This is a step-up transformer

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Step 2: Primary Current ($ I_1 $)

$$
P_1 = V_1 I_1 \Rightarrow I_1 = \frac{P_1}{V_1} = \frac{1800}{120} = 15 \, \text{A}
$$

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Step 3: Secondary Current ($ I_2 $)

From power conservation (ideal):

$$
P_2 = P_1 = 1800 \, \text{W}
\Rightarrow I_2 = \frac{P_2}{V_2} = \frac{1800}{1200} = 1.5 \, \text{A}
$$

Or via ratio:
$$
\frac{I_1}{I_2} = \frac{n_2}{n_1} \Rightarrow I_2 = I_1 \cdot \frac{n_1}{n_2} = 15 \cdot \frac{200}{2000} = 1.5 \, \text{A}
$$

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Step 4: Number of coils

- Primary: 200
- Secondary: 2000

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Step 5: Power

- Both sides: 1800 W

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✔ Completed Table 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: Output voltage = 1200 V

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## ✔ Final Answers:

Problem 1:

- Step-up transformer
- Secondary voltage: 2400 V
- Secondary current: 1 A
- Power: 2400 W

Problem 2:

- Output voltage at 75% efficiency: Still 2400 V
(efficiency affects power/current, not voltage in ideal case)

Problem 3:

- Output voltage: 1200 V

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Let me know if you want a version of the filled worksheet!